Climate science after Kyoto

With the Official Science monkey gone from our backs, what can we do with climate and climate science?

Over the last year, I've outlined on this blog a set of open questions that are frequently ignored and often not even seen correctly as questions, but that need to be answered if we're going to talk sense about "climate" and "climate change." Not able to predict weather beyond about two weeks ahead, we need a simplified and abstracted definition of "climate" whose "state" can be defined, analyzed, and predicted with some confidence. The fallacies of temperature averaging and "climate parameterizations" were a failed attempt to do this. Whatever notions of "climate," "climate state," and "change of climate state" we end up with will have to withstand - as temperature averages and the "hockey stick" cannot - probing criticism and emerge free of the hefty list of fallacies associated with the "global warming" hysteria.

In retrospect, the generational dead-end of climate and allied sciences with "global warming" and general circulation models (GCMs) can be viewed as an attempt to force a premature integration of theory and observation. It would be best for all involved if theory and observation were to remain aware of one another, but go their separate ways until such time as they have sufficient means to meet each other honestly. Until such a synthesis is possible, it's best to maintain a pluralistic and agnostic attitude about the Big Picture, resisting the forces bent on our "salvation" from the "evils" of industrial civilization or plying us with supposed alternatives to "knowing" nature.

What follows is a personal and partial view, informed by this failure to get a grip on these issues and by my own scientific experience along the edges of the problem and in related fields. It should not be taken as definitive or complete.

Theory: It's a really hard problem. The Earth's climate is the most complex scientific problem ever posed and almost certainly unsolvable in its full generality. Any progress we make with this problem will therefore necessarily involve approximations. The essential point is that, if we're going to attempt actual predictions, we need better and controlled approximations at every step. These are currently lacking.

Theory: Science is hypothesis and deduction. That is, it's not just a piling up of facts. Certainty of conclusions requires control of assumptions and reasoning.

There is thus an important role for mathematical deductive modeling, with simplified and controlled approximations applied at every step. The ideal should be to make these mathematically simplified and controlled models closer and closer, with each step, to the real climate. The failure of the "parameterized" GCM approach underscores the need to keep the modeling within controlled approximations at each step and not jump into the deep end of the pool right away.

Theory: Don't BS - simplify and smooth. A revealing way to look at the "climate state" problem is to grasp the motive behind "climate parameterizations": it was to "force closure" on the dynamical-structural equations of climate. In general, there are never enough equations to match the number of unknown variables. "Forcing closure" on the system means guessing or making up extra equations to close the gap.

But the gap could equally well be closed the other way: reduce the number of variables. A simplified "climate state," less complex than "the exact, instantaneous state of the whole atmosphere," is just such a proposal. It's also likely that such a state will not only involve flows and topology in space, but time and space integrals of the basic variables (equivalent to what statisticians call cumulants). Such integrals are usually better-behaved than the original variables.

Theory: Boil, mist, and trouble. Climate is chaotic, in the technical sense: exponential sensitivity to errors in initial conditions. Alternatively, climate is essentially nonperiodic, and not all climate disturbances die away. The atmosphere is a fluid, in the physicist's sense; its chaos is turbulence. Turbulence is the largest unsolved problem in physics. A partial or complete solution would have immediate impact on many areas of science and engineering, pure and applied, theoretical and practical - everything from understanding convection in planetary atmospheres and stars to improving your airplane or boat ride to reducing turbulence losses in your car engine.*

Climate needs new and better techniques for coping with chaos. Many such techniques have been developed in the last 25 years in various areas of science, but they haven't penetrated far into the climate world, partly because of the paralysis induced by Official Science. They include exceptionally relevant techniques like the following.

• Renormalization. This technique is a powerful generalization of the dimensional analysis we learned in school. (It's sometimes goes under the guise of "homology" or "rescaling.") It relates one mathematical problem posed at one set of space and time scales to a different problem at a different set of scales. Sometimes, impossible problems posed at one scales can be recast into other problems at different scales, and those different problems are solvable, either exactly or by controlled approximation.
  
  Renormalization for climate means imagining a scale at which decades, centuries, or even millennia seem modest and slow cycles like El Niño, say, wink by in rapid succession. On those scales, we can see more clearly the invariant and almost-invariant structure that must define, at a deeper level than everyday weather, what "climate" is.
  
  
• Dynamical reconstruction of phase space. This requires some contact with observed climate (see below), but the essential technique amounts to isolating the relevant degrees of freedom in the very complex climate system, the ones that operate on scales of tens to thousands of miles. Only a small subset of the possible changes in the climate system are actually important. Isolating them is a big step toward defining "climate" in a simplified sense. It will undoubtedly involve flows of heat, water, etc. (not local temperatures or humidities) and how they're connected in space (their topology).
  
  
• Non-Gaussian statistics, for extreme weather analysis. This is an application of the great progress that has been made in understanding how energy and other conserved physical quantities move through "open" systems, like the climate. Again, the issue straddles both theory and observation. People just have to stop assuming Gaussian (classical central limit or bell-curve) conditions in analyzing weather "events." There's never been any reason to do so.
  
  
• Pattern formation. This is an intersection of renormalization, non-Gaussian statistics, and "complexity," as an earlier posting discussed. The locus classicus for these techniques is understanding the perpetually landsliding sand pile. (There's even a cute book on the subject by Per Bak.) In complex, open systems with "flow-through" of air, water, and heat (or sand grains for that matter), long-range patterns with "almost" (but never quite!) repetitive behavior form and dissipate over and over - just like the weather: cyclones, storms, fronts, and so on.
  
  Pattern formation is especially germane to understanding clouds - their nature and lifecycle - better. Clouds are the most important feature of climate not easily captured by simplified models; convective turbulence is actually secondary in importance, at least for heat flow, although it's still crucial for the complete picture. And the big, difficult pieces of climate - clouds, turbulence, water transformations - are all linked together. Convection doesn't just transport heat; it lifts water vapor to higher altitudes than it would otherwise go, making clouds form more often and last longer than they would otherwise.
  
  The presence of clouds in turn transforms the climate by changing how radiation flows into and out of the atmosphere and providing a greatly enhanced form of upward heat convection. The main source of IR-active gas in the clear air is not CO2 or CH4, but the feedback effect of enhanced, clear-air water vapor. But even limited condensation of the enhanced water vapor into clouds changes the radiation flow drastically.

Observation: Go forth and squint hard. In the end, a chaotic system is its own best computer: no model we devise or limited set of observations we make can ever capture every aspect of its behavior. But observation nonetheless remains essential for understanding climate. Modern scientific observation of the atmosphere, increasingly detailed since the 18th century, has a lot to tell us about the repertory of possibilities.

In understanding actual climate, we must always keep in mind the proviso that chaotic systems feature an unending stream of unique events. We also have to face repetitive trends that repeat on time scales longer than the modern scientific record captures. Climate is, in this sense, a unique problem, in that we're inside the system being studied, and we're myopic observers with only hints and partial clues about the long term. Although laboratory experiments are essential for isolating general physical laws, the actual conditions of climate do not constitute a laboratory experiment. It's not controlled, and we're not outside the system in a position to aspire to know and control everything about it.

Observation: The Sun will have its say. It always does. It's the ultimate factor in charge of Earth's climate. Like other stars, the Sun is variable, at a small but measurable level. What limited observations have been made of our Sun already strongly hint at important solar modulations of Earth climate. The more basic solar physics in control here, and how the Earth responds to solar changes, are still poorly understood, and the whole problem remains at the frontier of research. But the base of raw data needed is now available in a way not true 20 or 30 years ago. Studying other planets' response to the Sun's variability will help.

Observation: All things green and blue. Plants and oceans need to be understood better as well. Over scales of decades and longer, they play a critical role in absorbing and recycling carbon dioxide. Current climate models capture the ocean part only imperfectly and plants barely at all. Yet there's a 0.2/0.00038 = 530 ratio of diatomic oxygen (O2) to CO2 in the air, which large ratio is made entirely possible by plant metabolism.** The annual plant-driven variations in atmospheric CO2 concentrations are about eight percent of the total. Since 100/(8/year) ~ 12 years, every CO2 molecule in the atmosphere gets captured by a plant in a little more than a decade.

What's not understood is how plants are responding in their annual cycle of growth and decay to increasing CO2 in the atmosphere. With more "food," there will be more and bigger plants. How much is unknown, although the Ice Age results give a very rough idea. What little research here has been done so far has been strongly tainted by people out to "prove" that plants aren't important - even though they clearly are. It's an obvious place for Gaia-philes to speak up. One of the few geoengineering ideas with any merit involves humans enhancing an already old and thoroughly proven means for removing CO2 from the atmosphere: more plants, bigger plants, maybe even über-plants. More on that next.
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* Indeed, the wild claims made by the IPCC for GCMs and "climate parametrizations" can be put into sharp relief when we consider that, were these results actually definitive answers for climate, we would also have a solution to fluid turbulence.

In fact, we don't. Over at the Clay Institute web site, you'll see there's a Clay Millennium prize for solving turbulence (Navier-Stokes equations) - and it remains unclaimed. Given the true state of affairs (turbulence remains an unsolved problem in physics and engineering), we can then rightly reason backward and conclude that the climate problem remains unsolved as well, since the turbulence problem is embedded within it.

** Without constant plant replenishment, the O2 would rapidly disappear from the atmosphere by oxidation weathering and water absorption. Animal metabolism would be impossible without plants, although plants can and, long ago, did do fine without us and our animal relatives.

Thoughts on the environment

Tout commence en mystique et finit en politique.

- Charles Peguy

Thinking about pollution as a public health problem and selective conservation of the natural world, for the sake of present and future generations, are in no way new endeavors. They arose toward the end of the 19th century, led by a variety of people who never dreamed of reading humanity out of nature or expressing hostility toward scientific understanding of nature, then emerging from its infancy. One of the best-known representatives of this movement - which predates the modern environmentalist movement by almost a century - was Teddy Roosevelt, who experienced raw nature first-hand, exploited it by hunting, wrote about it - and then created parks so others could taste the same experience. He was our first, and so far only, "environmental" president. There was nothing coffee-table-ish or armchair about his views, and he made his forays in the wilderness before cell phones, waterproof matches and tents, and other hi-tech paraphernalia were available. Today's environmentalist movement has moved far that orientation, representing a very different and basically mistaken view of nature and of humanity's relation to it. Environmentalism is a movement, not a science. The science is ecology, as practiced by ecologists. That hasn't prevented a long-standing and pervasive confusion between the two.

Born during the period that saw the breakdown of liberalism and its turn towards punitive and backward-looking guilt, the environmentalist movement started as a piece of counterculture and absorbed the older conservation and public health movements, usurping popular acceptance of the latter for its own ends. These ends are motivated by a hatred of technology, science, and modern civilization and bring in train all the classical fallacies of Romanticism: pre-existent "natural harmony," "noble savages," and the evil corruption of civilized humanity. Only once American civilization had reached a certain level of material development could such thinking take hold among more than a tiny number of the unbalanced. It's had a longer run in Europe, where it arose in the late 18th century in reaction to the rise of modern science, industry, and commercial society. The Germans gave a special twist to this thinking, one that merged nature-mysticism with reverence for the Volk and pre-industrial life.

The environmentalist movement has raided non-Western cultures and creatively invented bogus quotes about their attitudes toward the natural world. As shown by Dan Botkin and others, almost all of the supposed wisdom the movement peddles about natural "harmony" and "balance" comes from pre-modern and pre-scientific thinking within Western history, precisely the thinking that has been abandoned by modern science. (It wouldn't be modern or scientific otherwise.) The "pre-existent harmony" or "balance of nature" metaphor is the most common of these fallacies. Such discoveries as organic evolution and chaos (in the technical sense of the word) have forced ecologists to give up "equilibrium" pictures of ecosystems and face the reality of their ceaseless and usually messy change. Ecosystems come and go, start from a little, grow into a lot, mature into a period of glory - then fall apart and are replaced by something else. For example, it's precisely because the chaotic atmosphere and oceans have only a limited "invariant" structure that pinning down what "climate" means is so hard. So it has been throughout the 3.5 billion-year history of life on Earth; human activity just adds some more twists to the mix of permanent chaos.

But the "harmony," "balance," and "equilibrium" metaphors have, since the scientific revolution of the 17th and 18th centuries, taken on a life of their own, now divorced from scientific thought and philosophical criticism. They continued to be sustained by religious feeling and the rise of counter-Enlightenment Romanticism. It helps that the core of Western religious thought since the rise of Christianity has been the template of Paradise-Fall-Redemption, with perhaps an apocalypse in there somewhere. The relationship of environmentalism to this paradigm and the related concept of Original Sin is too obvious to require comment. So is the environmentalist hope that humanity's supposed trashing of the planet demonstrates that humans are still at the center of things, if only in a negative way. High German Romantic thought of the 19th century (with echoes and variations from the American Transcendentalists) recommended withdrawal from both human society and the five senses as a preliminary to communing inwardly with Nature - not the thing you can perceive, but a "telephone from the beyond," as Nietzsche wittily once put it.*

This is the paradigm of Thoreau's time living alone at Walden Pond, a Romantic exercise if there ever was one. He wasn't scientifically studying the ecosystem at Walden, getting his hands dirty. Not to put too fine a point on it, he was staring at his navel.** The root of environmentalism lies in a restless search for a new religion to replace older faiths no longer believable or relevant.

After the fallacy of pre-existent balance, the most powerful bad metaphor reigning over environmentalist thinking is its misplaced and often childish anthropomorphism and zoomorphism. Wild animals are not pets or farm animals, which are selectively plucked out of "wild" nature and bred by us to heighten characteristics that fit into human domestic and food needs. (After all, the wild ancestors of dogs could have been selectively bred to heighten other characteristics and turned into mean predators with no socially redeeming features.) Ecosystems and, indeed, the whole planet lack the integrated purposive and functional unity of individual animals and humans. It's a gross mistake to take metaphors like "Gaia" as more than fanciful poetic usages; the Earth doesn't think, feel, remember, or command anything.

But environmentalist literature and discourse are thoroughly polluted with such language and the concepts behind it. "Charismatic megafauna" (such as polar bears and baby seals) are projected as quasi-pets (instead of, respectively, hungry predators and their tasty, blubbery lunch). Gorgeous nature photography (itself a selective and superposed human art) is twisted into a "picture-window" or "don't-spoil-my-view" environmentalism that is really little more than middle- and upper-class kitsch. Debate about the human and non-human environments is mired in superstition and dishonesty if it assumes that nature would remain frozen were it not for our interference. It becomes enlightened and honest when the question shifts to, "Well, what do we want it to look like?" Not that we always get our wishes - but they're our wishes, not nature's. Nature has none.

If we're interested in a scientifically-informed view of nature and our relationship to it, we must abandon any notion of pre-existent "harmony" or "balance" that we are violating, restoring, or revering as an authoritative command. Nature commands nothing and speaks nothing. Or - better - it speaks many contradictory things: it's prodigious, wasteful, and hidden; beneficent and poisonous; abundant and barren; peaceful, aggressive, and indifferent - all at once. It is relentless change, on all scales of space and time, with incessant destruction, creation, and overturning. Any harmony or balance we bring to our relationship with nature is a balance or harmony strictly of our own devising. We're not even "managing" nature, except in a limited way. In limiting and modifying how we use nature, we really managing nothing but ourselves.

That is why environmentalism is not science, but a political and religious movement. It is why this movement so frequently turns tyrannical: there's nothing so satisfying to a fanatic than "managing" other people as a vehicle of righteousness.† Perhaps this is the unwittingly ironic sense in which Job urges his friends to "speak with the Earth, and she will teach you." She will teach you all right: she'll teach you that she has no trite moral lessons to offer. Equilibrium, balance, and harmony are not the norm, but temporary and local. Indeed, at the center of Job's encounter with the divine is, not a garden or a zoo, but a whirlwind.

In absorbing and condescending to the older public health and conservation movements, the nearly forty years of modern environmentalism have done our society a large disservice. It is the most potent social force today in attracting the general public away from science. Scientists involved in ecology themselves often lead mentally conflicted lives, caught between knowing and believing. People now routinely use meaningless or wrongheaded concepts to misunderstand the world around them and how human activity affects it. Recycling is often more harmful than just throwing things out. No one has a "carbon footprint," unless they've rubbed graphite on the bottom of their shoes. The Earth's climate is not a greenhouse. Nuclear power plants are not bombs, any more than a coal-fired power plant is a firearm. Runaway metaphors and bad policies motivated by them are the fallacies of the Boomers - history's first mass over- and miseducated generation - and now constitute the brainwashing of the next generation. Led by their delusional gurus, currently starting with Al Gore, they have injected a potent revulsion against modern technological and progressive civilization into our politics.†† But that passion proves nothing about the rightness of their cause, which is essentially romantic, pessimistic, and reactionary.‡

POSTSCRIPT: For an example of what I'm talking about, consider M. Night Shyamalan's embarrassing new movie, The Happening, "the most morally abhorrent film ever made" - but still, important for laying bare the logic, which pervades conventional environmental politics in a watered-down form. Or just read this New Republic blog posting and skip the film itself :)

POST-POSTSCRIPT: Everyone interested in this problem, whatever their opinions, should read Wallace Kaufman's No Turning Back: Dismantling the Fantasies of Environmental Thinking. Published 14 years ago, it is more relevant than ever, and a blog posting cannot do it justice. In related vein, consider as well the two books by Alston Chase, In a Dark Wood and Playing God in Yellowstone.
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* While not able to speak English, Nietzsche could read it and counted an edition of Emerson's works as one of his prized possessions; he annotated it, heavily in places. His famous Übermensch, or Overman, probably owes something to Emerson's Oversoul. I don't know if Nietzsche read any Thoreau.

** That said, I like Walden Pond as it is now and try to swim it at least once every summer. There's been no attempt to "freeze" it in some mythical past, and it is accessible by car. It was pretty accessible in Thoreau's day, and he was never more than an hour walk from the center of Concord and medical and food supplies. Thoreau even took his laundry home to his mother for washing periodically. The old railroad line, already in existence when Thoreau spent his two years there, still runs right past the pond, behind some trees. Even more than in Thoreau's day, the setting now is as much a product of human artifice as it is of nature and a perfect example of the older conservation movement - but not of modern environmentalism.

† Thoreau himself said it: a man feels a disturbance in his bowels - and he sets off on a crusade to save humanity.

†† Using "progressive" again in the right sense.

‡ The absolute weirdness of our political vocabulary strikes me more and more. Opponents of environmentalism are usually called "conservative" - are they, really? And is environmentalism really "liberal" and "progressive"?

Thoughts on pollution

"Pollution" can mean different things in different contexts. Here it means something in the human environment that causes harm to humans. Since that can include both natural and manmade things, let's narrow it further to manmade. Finally, to exclude the obviously different situation of someone deliberately trying to poison someone else, let's narrow it further to the inadvertent, the "side effect" of otherwise beneficial activities. Economists call these "external costs." It's what happens when I throw a party on my lawn, pay for the party, but leave my party trash on your lawn for you to clean up. If it's a result of routine, repeated activity, we have what people usually mean by "pollution."

There are four ways to deal with pollution:

• Harmed party takes harming party to court after the fact. This works for something that happens once or very occasionally. Otherwise, it's pretty cumbersome.
• If it's a routine occurrence, government regulates the level of emission of the pollutant. This often works, but depending on the type of pollutant and available technology, it can be difficult or very expensive to continue the polluting activity and limit the polluting side effect.
• If it's a routine occurrence, restrict the use of the pollutant or ban it entirely. This is sometimes feasible, occasionally desirable, but again often expensive or difficult if the underlying polluting activity is to keep going. If that activity is otherwise beneficial, this is hard to justify.
  
• Tax the emission of the pollutant and leave it up to the polluter to figure out the best way to limit the emission. Unless something should be tightly restricted or banned, this is usually the best approach, because it's the least cumbersome and most flexible. Ask an economist how to deal with pollution, and that's most likely the answer you'll get.
  

Governments around the world have spent more than a century coping with the side effects of modern economic development in these ways. In pre-industrial societies, there was pollution too, of course: think of all that horse manure in the streets. But it was on a generally smaller scale and, crucially, no one cared or understood enough to do anything about it. The modern public health movement started in the second half of the 19th century to deal with these side effects of development, because the understanding was there, for the first time, and the scale and concentration of the problem were bigger.

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When a pollutant (defined in this way) is around us, how do we gauge its potential for harm? The essential answer is concentration times exposure. The more concentrated it is, the longer we're exposed to it, or both, the more harm. The exact concentrations and exposure times vary from pollutant to pollutant and, to a lesser extent, from person to person. Concentrations in the environment generally fall with time, if the pollution source is stopped.

Some important conclusions follow.

The first is that the most harmful things we are exposed to are the things we do to ourselves. After all, we're exposed to ourselves all the time, and the things we put into our bodies ourselves are generally the most concentrated things we encounter in everyday life. The most obvious, and deadly, is smoking, whether it's tobacco or something else. The smoker is getting a certain pleasure out of it, but the harmful side effect is large and cumulative. Living as we do in a society that likes to think of itself, at least, as free, we inconsistently allow people to do some harmful things to themselves, but not others. It's usually a bad idea to try to stop people from doing such things by force, because force rarely works over time. But that doesn't mean we can't nudge people in the right direction. And it means governments have no excuse for, say, subsidizing growing tobacco.*

The second is that home, school, and workplace hazards are the next on the list. These are the places we spend the most time and often have limited control over and knowledge of what we're exposed to. If the hazards are routine, there's a good case for legal regulation. But where and when we do have control, there's an even stronger case for exercising common sense.

The third is that everything else is generally less important. The reason is that, whatever the exposure times, the concentrations are much lower. Cut off from its source, chemical pollution disperses and transforms over time. Of course, if you live next to a smokestack that's going all the time, say, then you're closer to the "workplace" situation. And occasionally, nature itself mixes in with manmade pollution to concentrate the problem, instead of dispersing it. The classic "smogs" that used to form over industrial cities (smog being a mix of natural dust and water vapor with manmade smoke) are one example. Another familiar to residents to Los Angeles and Mexico City is vertical atmospheric temperature inversion (remember that from last year?), which can trap smoke and other aerosols that would otherwise disperse.

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Dividing the world up into the categories of "harmful, neutral, and beneficial" to us is completely separate from dividing it up into the "natural" and the "manmade." Nature has lots of harm out there is store for us if we're not careful. Bacteria blindly doing their thing can sometimes kill a baby or an adult. Insects, snakes, and plants sometimes have deadly poisons. Floods and storms can destroy what we've built and kill us. Certain plants have dioxin-like chemicals no different in their harm from the harm done by artificial ones. There's no malintent involved, although much of what's true about manmade pollution harming us is also true about an insect bite or allergen harming us. Our bodies themselves have defense mechanisms against the harm, at least up to point. How are bodies react to these things is a function only of our bodies and the harmful agent - whether or not it was manmade, whether or not it was the product of evil intent.

Until around 1970 or so, such distinctions and commonalities were taken for granted, and much of the time, they still are today. The rise of the modern environmental movement around 1970, however, changed how we think about these issues, deeply confusing them together, blocking out simple truths about nature that our ancestors had no problem seeing, and injecting agendas into our politics that are superficially about one thing (public health, say, which wasn't discovered by the environmentalist movement) but are really about something else entirely (like stopping economic development, no matter what the harm to humans, or punishing private economic activity simply for being private). The independent distinctions of "natural-manmade" and "beneficial-harmful" were merged. Side effects of civilization, and ultimately civilization itself, were demonized as the results of harmful intent. Since about 40 years ago, such thinking, the groups that promote it, and the politicians who pander to and depend on it, have done real harm in the most advanced countries, especially in the ultra-litigious US. More recently, environmentalist groups and politicians have tried to confuse the subject further by peddling the wishful thinking that regulation (of any kind, beneficial or not) has no or minimal costs. That can't be true; otherwise, people would implement the practice themselves. Even beneficial regulation has costs, but we enjoy the benefit (if it is actually beneficial), and its cost can often be offset by economic progress elsewhere. In poor countries, those options are often not available, and terrible harm has been inflicted there, by denying them (for example) pesticides and, more recently, selectively bred crop seeds that reduce the need for pesticides. The cumulative effect of such abuse of government power is major and persists if nothing is done to reverse it. Such a movement is not about public health, clearly. And it is a movement, not a science.

Economic valuing is based on benefits, costs, and harms to someone. It's meaningless to discuss benefits and costs outside that framework; there are no "intrinsic" costs and benefits without a party benefited or harmed. Since nature as a whole has no "body," no intentions, and no "health" the same way an individual human or animal has, the environmentalist movement has to operate on a metaphysical plane, even as it abuses political and social mechanisms designed for strictly human use. While it claims to speak for "nature," it really speaks for no one but itself.

"According to nature" you want to live? O you noble Stoics, what deceptive words these are! [Stoicism was an ancient philosophical school that exhorted its followers to "live according to Nature."] Imagine a being like nature, wasteful beyond measure, indifferent beyond measure, without purposes and consideration, without mercy and justice, fertile and desolate and uncertain at the same time; imagine indifference itself as a power - how could you live according to this indifference? Living - is that not precisely wanting to be other than this nature? Is not living - estimating, preferring, being unjust, being limited, wanting to be different? And supposing your imperative "live according to nature" meant at bottom as much as "living according to life" - how could you not do that? ....

In truth, the matter is altogether different: while you pretend rapturously to read the canon of your law into nature, you want something opposite .... Your pride wants to impose your morality, your ideal, on nature ... you demand that she should be nature "according to the Stoa," and you would like all existence to exist only after your own image - as an immense eternal glorification and generalization of Stoicism. For all your love of truth, you have forced yourselves so long, so persistently, so rigidly-hypnotically to see nature the wrong way, namely Stoically, that you are no longer able to see her differently. (Nietzsche, Beyond Good and Evil, 9)

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* While trying to discourage its use. That means that the tobacco has to be exported to other countries. Which it is, and that's government-subsidized too.

Climate reservoirs and budgets

Often we hear phrases like "balance of nature" that imply a natural stasis in the world. It's an old idea, occurring in all human cultures, and running in Western thought back to the ancients and beyond, Plato and Aristotle the most influential. Although the concept of natural stasis has been abandoned by modern science, there is a more limited but precise and up-to-date version of this concept - we've met it before as conservation laws or symmetries.

The role of conservation laws in complex systems is sharply two-faced. On the one hand, what invariant structure they have - what remains over time - is tied directly to these laws. On the other, complex systems typically have such a vast number of variables (degrees of freedom) - think of the weather, or of an ecosystem, or the global economy - that the number of conservation laws is far too few to put much of a constraint on how such system can evolve over time. That is why such systems usually behave in chaotic ways ("chaos is weakly constrained") and exhibit the classic pattern of complexity, the spontaneous formation and dissipation of structures.

Everyday conservation laws. The conservation laws important for the climate (air-ocean system, essentially) are familiar from earlier postings and perhaps from chemistry class. They include conservation of total mass, of individual atoms, of energy. More specialized and qualified forms include conservation of air, water, and heat. For a simple system of a finite number of degrees of freedom, conservation laws take the form

function of variables = constant, or change in conserved function = 0

For a continuous system of flows in space, the conservation law takes the form

flow out of a volume - flow into that volume + change of quantity in volume = 0

For "quantity," substitute mass, number of each atomic element, energy, etc. If you draw the boundaries of the volume the right way, so that there are no flows into or out, the conservation law becomes

change of quantity in the volume = 0

There's nowhere for it to go.

Still useful even if not exact. More generally, "partial" conservation laws are useful for quantities that are not conserved, but can still be tracked by what essentially amounts to an accounting device. For example,

flow out of volume - flow into volume + change of quantity in volume = quantity transformed within volume

For example, chemical or phase changes might make certain quantities exactly conserved (like the number, each, of hydrogen and oxygen atoms and water molecules), while others might be subject to transformations that proceed at a certain rate: for example, particular forms of water - solid, liquid, vapor - which are not separately conserved, but transformed into one another in such a way that the number of H atoms, O atoms, and H2O molecules each remains unchanged.

Symmetry, identity, conservation. And that's why conservation laws are related to symmetries. A symmetry, to a mathematical physicist, says, the system does all sorts of things as it evolves, but certain aspects of it retain a constant identity. The game is then to identify what those "invariant" aspects are. In other cases, certain "almost exact" identities can be picked out and used to make approximations.

Conservation laws and climate. Such conservation laws, in their "spatial flow" forms, are the foundation for understanding climate as an "accounting" system: so much air and water (never leaving or being added to - the climate system is "closed" with respect to air and water), so much heat flowing in and out (the system is "open" with respect to heat flow), so much radiation flowing in and out.

Applying these laws correctly means having to identify "reservoirs" of air, water, radiation, heat, etc., some of them truly closed, if you draw their boundaries correctly; some of them only approximately closed; some of them truly open. It also means identifying flows correctly. For example, "global warming" (enhanced infrared-active gases in the air) changes the flow of heat upward in the atmosphere, but it does not trap heat in a fixed volume in the lower atmosphere. This is perhaps the most exact way to state that fallacy.

Another example is water, both the total amount and flows from one place to another. The amount of water in the air-ocean system is almost conserved; there are some slow geochemical reactions that take water out of the system.* But eventually, that water is recycled, reappears in volcanic eruptions, and gets re-injected into the air-ocean system. That points to another consideration in correct application of conservation laws, that of time scale. Something might be taken out that eventually gets put back in. And the geochemical reactions themselves might be so slow and at such a low level that water in the air-ocean system might as well be considered exactly conserved to high accuracy, over shorter time scales.

A year ago on this blog, conservation law reasoning was used to conclude that an enhanced evaporation rate (from, say, "global warming") would lead, not only to more clear-air water vapor, but necessarily to more condensation, clouds, and precipitation: necessarily, since the water is not escaping into space. So it has to come down, at the same rate it's going up, if we sum over the whole atmosphere.

For truly open systems, on the other hand, it's better to think of the flows as providing a daily or annual "budget" of sorts: so much radiation in per day, so much heat out, and so on. The radiation-heat flow is determined by the Sun's output, which itself is not exactly steady. The climate "works with a budget" that's not exactly the same every day or every year. Another example is water flow, considered not on the scale of the whole planet, but within some limited ecosystem. This system might have water "reservoirs," to use the word in its everyday sense; but these reservoirs are open, not closed, and dependent on direct rainfall and ground flow. Because they're open, such reservoirs will not, in general, be faced with even an approximately steady flow in and flow out. Their "water budgets" vary much more wildly.

POSTSCRIPT: The last solar magnetic activity cycle (the one that peaked in 2001) should have ended last year. Typically, the next couple years see an upswing of activity: sunspots, solar wind "gusts," the new cycle's first solar atmosphere mass ejections. But not this time. The peak should be 2011 or 2012. So far it's unusually quiet.

Such periods of extended or exceptional solar quiescence are almost always associated with somewhat colder temperatures here - which is just what we've been seeing the last year or so. (Hat tip to Instapundit.)
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* An example is the set of reactions mentioned here last year as removing carbon dioxide from the atmosphere into the oceans. It starts with dissolution of CO2 gas into CO2 bubbles in the water by diffusion, over roughly a 10-year time scale, with an almost equally fast outgassing of CO2 bubbles back into the atmosphere. CO2 molecules are conserved at this step, but not the next. The water (H2O) then reacts with the CO2 to form carbonic acid (H2CO3). A CO2 and a water molecule are destroyed in the creation of one carbonic acid molecule. But the number of C, the number of O, and the number of H are separately conserved.

Then the fun starts. The H2CO3 dissociates in the water, as all acids do, into H+ and HCO3-, then into 2H+ and CO3--. (The + and - are electric charges.) The opposite reactions occur at the same rates, but the CO3-- is also slowly but steadily removed altogether by binding over century or so timescales with ocean salts: potassium (K+), calcium (Ca++), and magnesium (Mg++), all with some positive charge.

The resulting minerals - calcium carbonate (CaCO3, or limestone, chalk, etc.), magnesium carbonate (MgCO3, or dolomite), and potassium carbonate (K2CO3, or potash) - sink to the ocean floor, where, many, many millennia later, they end up contributing to the natural release of CO2 and H2O from volcanoes back into the atmosphere.

Entropy, information, and the ice cube

Looked at the right way, a humble ice cube can teach you a lot about thermodynamics. As Nicholas Taleb points out in The Black Swan, the simplest facts about how it melts contain the kernel of the Second Law of thermodynamics by implication. Elaborating upon the simplest case illuminates many other situations far more complex.

The Second Law is not deterministic, but probabilistic. It doesn't say, the system has to evolve in such and such a way. It just indicates, given where a system is now, what the most probable direction it will evolve in. Thermodynamics comes into play when we can't know the exact state of every water molecule. Instead, all we know are certain fixed totals about the system: the total energy, the total volume, the total number of molecules. In the very simplest case, total isolation, the ice cube does nothing.

In the next simplest case, the cube is isolated except for contact with a heat bath, which is defined by a temperature, which we'll assume is at or above the ice melting temperature. The Second Law tells us the overwhelmingly probable evolution of the cube: it will change in the direction that increases its entropy or disorganization. That includes heating up (acquiring heat from the heat bath). In this case, that includes melting.

When the entropy increases, information is lost. Imagine that the ice cube has some features on its surface, or that it was carved into some shape. After it's fully melted, all that's left is puddle of water. The puddle of water is the final result, regardless of whatever funky features the solid ice had in its shape.

Since its discovery in the 19th century, the Second Law has had a sad countenance, apparently nothing but a tale of decay and decline. Certainly the thought that an elaborately carved ice sculpture and a plain ice cube of identical mass might end the same way - as a large, featureless puddle of water - made thermodynamics seem like the truly dismal science.

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But these are only the two simplest possibilities for the ice cube. It could be in contact with a chemical bath of some substance that reacts and binds with water (hydrates). In that case, two processes, melting and hydration, proceed simultaneously. The larger and/or faster will predominate, since it increases the entropy faster. Melting might not happen at all, because the Second Law would then have another and better avenue to satisfy itself. The Second Law doesn't tell you that melting has to happen; just that, whatever avenues of change are available, the one that gets you to higher entropy faster wins. And it only specifies a probabilistic tendency, specifying nothing in general about rate, except that it's positive.

By historical convention, systems in passive contact with external "baths" are not considered "open." They are in thermodynamic equilibrium with themselves and any "baths" in contact. Truly "open" systems are ones with "flow-through," where matter, radiation, and/or heat flow in and flow out. "Open" systems are not in equilibrium, in general, either with themselves or with the outside. In that case, the Second Law still applies, but it only applies to the whole system and its environment. Any part of the whole can see its entropy decline, so long as the entropy of the whole rises. If an open system exhibits a strong spontaneous tendency under certain conditions to lower its entropy and acquire structure, it has to expel the excess entropy outside of itself. The system is said to be self-organizing.

Hence, biology, evolution, and weather.

The competing rates of different processes become a more complex but even more critical tangle in the self-organizing case. For self-organization to succeed, the spontaneous structure has to form faster than any competing process (dissipation) importing entropy back into the system from the outside. Thermodynamic equilibrium is not valid for "open" systems as a whole, but might be valid for parts of the system. Typically, equilibrium is an excellent approximation for suitably "small" part of the system, where local temperature and pressure can be defined and local thermodynamic equilibrium (LTE) holds. But it remains true that on intermediate to the largest scales of the system, LTE is badly violated. These are exactly the scales over which flows of matter, radiation, and heat are most obvious.

One of the things that makes weather and climate prediction so hard is that on intermediate to large scales, the evolution of the atmosphere is not, on the one hand, a simple application of determinism: the system is chaotic; but on the other, not a simple application of thermodynamic arguments either. On short scales (a few to a few tens of meters), the atmosphere respects LTE pretty well, and thermodynamics can be used to predict its evolution (if boundary conditions are known). But on the scales of storms, cyclones, and fronts, the atmosphere, while "thermodynamic" in some sense, is nowhere close to thermodynamic equilibrium, and the simple probabilistic arguments of thermodynamic equilibrium don't apply. It's chaotic enough to make long-term, detailed prediction impossible; but not so chaotic that simple statistical arguments can be used instead. It's somewhere in between: highly sensitive to poorly known initial conditions and past history.

This realm - in between simple linear predictability and simple statistical equilibrium - is not only a result of chaos, but constitutes a distinct area of dynamics and physics, usually given the name complexity. It's a dynamical regime rich with unpredictable structures that repeatedly form and dissipate - like weather, or living things. (June 2)

POSTSCRIPT: The conventional global temperature index continues its recent precipitous drop. In case you've been hiding in a basement the last few months, this was the coldest spring, and the coldest May, in many years.

It should be stressed again that this conventional global temperature index (one of a handful of composite statistical indexes used by the IPCC and others) is not the temperature of anything. The Earth has no single temperature: it's not in thermal equilibrium, with either itself or a "heat bath." It's a complex weighted statistical composite of many individual temperature measurements of the air, ocean surface, and radiation. (The first two are local; the third is nonlocal, by its nature.) The attempt to pass this composite off as the unique "temperature of the Earth" is one of the many major fallacies of the climate change hysteria.

The direction and timing of the trend are not in doubt. Something has been happening in the last decade and has accelerated. That something is cooling. But the exact nature and magnitude of the trend can only be understood by disaggregating the composite index back into its originating individual temperature measurements and looking at their trends in time and space.

The black hole of climate parameterizations

The theoretical band-aids used to "fix up" climate models after the butchering of the full theory produce a final mishmash, chunks of climate theory rounded out and connected by uncontrolled simplifications of physics too hard to solve, with details filled in with selected past behavior.

The patching up of conservation law violations and filling in for unsolvable turbulence and water dynamics are accomplished by "climate parameterizations," the rather embarrassing ad hoc-ery inherent in all present-day state-of-the-art climate modeling. Climate parameterizations are an unavoidable corollary of the GCM method. Each climate model "cell" produces a wrong answer, with no estimate of error. Somehow the sum total of these is supposed to produce a globally "right" answer. Regional climate models have even larger problems, because the climate specification on the boundaries of each "cell" is undefined to start with. If anyone comes up with the right answer using this procedure, it's strictly by luck.

These parameterizations "force closure" of the climate dynamics within each cell. "Subgrid" processes are not tracked. Instead climate parameterizations replace the missing dynamics on scales smaller than the grid resolution. They substitute for the dynamics on all but the largest spatial scales (hundreds of miles, too large to resolve even a hurricane), hiding essentially all of the chaotic behavior and most of the full hydrologic cycle (GCMs include simplified evaporation, but not condensation or precipitation dynamics). Some of these parameterizations are based on "reasonable" theoretical conjectures. But most are based on observed climate data - that is, on past climate behavior.

Briefly, there are at least three things wrong with these parameterizations.

1. Causality is eliminated within the grid cells. Cause-and-effect relationships unfolding in space and time are replaced by static, algebraic relationships. Subgrid dynamics disappears: chaotic turbulence, much of convection, condensation, cloud formation, and precipitation. Most of the self-organizing phenomena characteristic of our atmosphere are not dynamically simulated.

2. Past performance is no guarantee of future results. The climate system changes on time scales longer than modern climate data can capture. And it's also chaotic, shot through with unique, one-off events that never repeat. By using past climate data, climate parameterizations take an uncontrolled slice through the space of all possible weathers, essentially assuming that all possible weathers are represented by the time- and space-limited pool of available measurements. But this pool is restricted in time, in the spatial and temporal resolution and comprehensiveness of available data and, by its nature, cannot capture climate chaos.

Such an approach amounts to Fourier analyzing the complete climate evolution in space and time, then chopping out all but a limited range of time and spatial scales. The rest is missing, and that pesky chaos at zero frequency has been excised away. But climate processes at different spatiotemporal scales interact with one another, transferring energy, momentum, air, and water from larger scales to smaller and back, as weather features self-organize and dissipate.

3. Circularity of reasoning. To make predictions for a dynamical system, one ideally starts with a complete, defined theory, adds initial and boundary conditions, then solves for the answer. The results can be "cleanly" compared with measurements to see if the theory and any approximations made in solving it were right.

By using past climate data in defining the theory itself, we're "contaminating" the predictions of theory with the "already known answer" - cheating, in effect, although the cheater has copied a probably wrong answer. It's not a "clean" test by any means. In practice, global and regional climate models are continually adjusted to match observed climate. The resulting model looks "right," but that's an illusion. It's actually a massive case of what statisticians call "confirmation bias." The model has been adjusted to retroactively reproduce past behavior. There's no way to know if it can predict future behavior. More likely, the model will have to be readjusted again, the day after tomorrow, to "retrodict" tomorrow's weather.

The illusion of an answer. You might wonder why climate modelers ever got into what looks like a dead end. The answer is that there aren't, at present, good alternatives to this program of climate modeling approximations. Basic questions would need to be revisited and re-examined from scratch. This is a great open and urgent question in climate theory. The resources that such questions should get are instead used up in chasing illusory improvements in ever-larger and dubious GCMs. More computer power and memory can't solve this problem. It's the modeling procedure itself that's wrong. Better computers will just produce meaningless results more quickly.

While there are climate modelers and scientists guilty of overselling and misrepresenting the reliability and completeness of the GCM program, that sin pales into comparison to the main force behind this drive round and round the climate modeling cul-de-sac: it's political, not scientific. Certain political figures (not just elected politicians, but science policy and bureaucratic types as well, and the eco-fanatics) have a strong (but probably wrong) preconception of what's going on with climate. They want "correct" answers. In a larger sense, the general demand for definitive climate predictions of any kind is the more basic culprit.

The modern GCM approach to climate modeling began in the early 80s and has never left its infancy. By the early 90s, it was very prematurely "drafted" into providing pseudo-definitive climate answers. But in their current form, GCMs can never produce the answers sought or falsely claimed.

POSTSCRIPT: Essex and McKitrick discuss the full range of climate modeling fallacies in considerable, but not overly technical, detail. Leroux and Comby discuss the topic even more extensively, at greater technical depth.

Climate models: What went wrong

You shall not curse a deaf man, nor place a stumbling block before the blind ....

- Leviticus 19

Climate models of any kind, including GCMs, involve multiple layers of approximation. They are not the full theory. That is unsolvable and cannot even be properly stated in its full complexity, which is why climate models are used in its place. From a mathematical point of view, the key question is the nature of those approximations.

On the grid. The most obvious approximation is the discrete spacetime "grid" that replaces the spacetime continuum. A continuum and any field on that continuum (pressure, temperature, etc.) contain an infinite amount of information and cannot be represented by a finite list of numbers and thus on a computer. The first step is to replace the continuum with a grid of discrete points in space and instants in time.

A set of thermohydrodynamic variables (pressure, temperature, wind, water) is solved for within a grid cell. In place of variables that are functions of continuously varying time and space, we get discrete points and instants. The continuous integrodifferential equations of physics are replaced in the model approximation by discrete difference and sum equations. This approximation gives rise to discretization error, which is bounded and can be controlled by making the space and time cell size smaller. Hence the quest for ever more computer memory, to handle larger and larger numbers of smaller and smaller climate "cells."

However, this approximation is far from the only one inherent in climate modeling. The mistaken assumption that it is feeds the illusion that bigger computers are all that's needed to reduce the uncertainties. Given the immense complexity and chaotic nature of climate, it's also not the case that bigger computers are a practical solution even for just this modeling error. Attempts to forecast weather over weeks and months have consistently led to the conclusion that computers much larger than any built, calculating for times longer than the lifetime of the universe, would be needed to cope with weather chaos, which in climate manifests itself as atmospheric turbulence.

Poorly defined statistical averages. In place of dealing with chaos directly, climate models sample sets or ensembles of initial conditions, then average over the samples. The climate modeling fallacy arises from this averaging over undefined model spaces. No one understands the full climate theory well enough to enumerate possible climates and assign them probabilities. (Mathematically, there's no "measure on the space of models.") How do you average? How do you know you've got a representative sample of the space of possible "weathers"? No one knows. The workaround today is more ad hoc handwaving, making convenient simplified assumptions there's no way to check and which further butcher the theory.*

Forcing closure on the equations. Discretization of continuous spacetime gives rise to other, more technical modeling errors as well. These additional approximations fall into two broad classes, although these classes of errors interact with each other.

1. Inherent in the complete theory of climate are continuous symmetries of the laws of physics. These laws are independent of translation in space, rotational orientation, and what time it is. Each gives rise to a conserved flow: densities of momentum, angular momentum, and energy. When the theory is discretized to form the numerical approximation, these symmetries are broken and the conservation laws violated. These violated conservation laws (momentum, angular momentum, and energy appearing from and disappearing into nothing) have to be "fixed up" in some way, so as to not produce nonsensical results. These "fixing up" methods, which we'll meet in the next post, themselves introduce ad hoc and uncontrolled approximations.

2. The unchanging identity of a parcel of dry air and a parcel of water gives rise to further conservation laws, relating the flows and densities of water and air. The full theory of climate includes within it the hardest equation of physics, first discovered in the 19th century, the Navier-Stokes equation. It describes the dynamics of fluids (air and water, both in gaseous and liquid states - physicists use "fluid" for both). These equations cannot, even on their own (without the effect of radiation and of the phase transitions of water from ice to liquid to vapor), be solved or even be stated in complete form. Instead, fluid dynamicists in physics and engineering introduce simplified approximations ("forced closure") to covert the fluid dynamics into something that can at least be stated as a complete, self-consistent mathematical problem. Introducing the phase transitions of water and the radiation passing through, being reflected, absorbed, and re-radiated, makes the problem even more intractable. So further approximations (more "forced closures") are introduced.

From a mathematical point of view, these "forced closures" are not controlled approximations. There's no way to bound or estimate the error made in introducing them. In laboratory or engineering applications, we have an "out," namely, controlled experiments that provide an alternative source of insight into the behavior of fluids. We have no controlled experiments for the atmosphere, with its mix of air, discontinuously changing water, and radiation.

Known unknowns and unknown unknowns. Reliable knowledge in the sciences arises from controlled contexts: deduction from explicit assumptions, laboratory experiments, mathematical approximations with bounded errors. In such situations, even if we can't arrive at an exact answer, we know the right questions to ask and get a range of the numerical values we seek. In climate modeling, we are lost. Not much has been attempted in the way of rigorous deduction from the full climate theory, partly because it's so complex. We have no controlled laboratory experiments. And the leap from the full, unsolvable theory to any known model (including the GCMs) is made with uncontrolled approximations. We might know the right question to ask, but have a only vague idea of the numerical range we're aiming for - perhaps on the order of five or so degrees C. It's quantitatively too fuzzy to serve for the kinds of precise conclusions that people seek, temperature changes on the order of tenths of degree C, or even a full degree.

What is climate anyway? And there's a more basic problem: we don't know what "climate" means, unless it means the exact state of the whole atmosphere and oceans at one instant. That's far too vast to comprehend or measure, and it might not even be necessary to know all of it. What's lacking is a reduction of "climate state" that can serve as a simplified abstraction to track. Such a state would need to track something about the state and flow of the air, the heat, and the water. There's no "temperature of the Earth," in spite of the meaningless numbers bandied about. All such intensive thermodynamic measurements are local and vary in space and time. We need something that captures the spatially spread-out nature of climate and the fact that it's controlled by flows, not static reservoirs, of heat, air, and water.

Just as there are few controlled approximations in modeling climate dynamics, there's no controlled and well-defined "state" of climate even to talk about. These are open scientific questions. Unfortunately, they're almost always taken as somehow already answered or are never even asked. But they need to asked, and we need to face the fact that, at present, there are no good answers.

POSTSCRIPT: Chapter 3 of Lorenz's chaos lectures discusses the origins of GCMs from the point of view of someone who was there.
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* Readers of this blog might remember this problem from over a year ago in a very different context, the failure of the "multiverse" or "landscape" picture of string theory. There was no way in that case to specify a list of universes and assign their probabilities either.

Climate models: Their origin and nature

An infinite number of approximation schemes are available to turn the full climate theory into something tractable. In practice, approximation methods have fallen into a few distinct classes.

Textbook cases. There are very simple approximate models that can be solved exactly. These typically exclude convection and include evaporation, condensation, and clouds only in a very simplified form, if at all. Such models are frequently used in climate textbooks. A slightly more complex class of models require computers to achieve an approximate (but typically quite accurate) solution. (That is, the theory is replaced by an approximate model, which itself is then subject to further approximations in order to solve it.) The earliest versions of both classes of models date from the end of the 19th and the early decades of the 20th centuries.* Early versions of numerical approximations, which replace continuous time and space with a discretized "grid" of time instants and spatial points, were developed during these periods. The calculations to implement these approximation methods are tedious and had to be done by hand. (In the 19th century, a "calculator" was a person who carried out this arithmetic drudgery!) In the 1920s, 30s, and 40s, electromechanical calculators, forerunners of today's electronic handheld calculators, were pressed into service to carry out such work. It is worth stressing: the computers just implement a numerical approximation scheme; they do no physics and don't "know" the approximation method except to the extent that they are programmed by humans.

The rise of large-scale computer models. Around that time, the British physicist Lewis Fry Richardson, following up the suggestion of Norwegian Vilhelm Bjerknes, collected the pieces of the full climate theory as we know it today. The fluid dynamics and thermodynamics of air and water vapor were discovered during the 19th century, including the famous Navier-Stokes equation, which describes the motion of turbulent fluids. At the end of that century and the first decade of 20th, the nature of radiation and radiative heat transport came to be understood for the first time. With all these necessary pieces, Richardson wrote down a simplified version of the complete climate dynamics. He postulated that hundreds or thousands of human "calculators" could be set to doing the necessary arithmetic to implement a numerical "grid-ified" approximation scheme for the atmosphere.

From the start, Richardson's first attempts to predict weather ran into just the problems that would subsequently occupy climate and atmospheric scientists for the rest of the century. He could never piece together enough initial condition information to properly start the integration forward in time. He ran into a version of chaos, although he failed to understand the full nature of what he had stumbled into. The human-implemented arithmetic calculations needed to carry out the method were so slow that weather prediction could not be done in real time. Starting on day one, he got to making a prediction for the following day's weather only after six weeks - and it was wrong. Richardson had posed the full climate problem, for the first time, as a problem in mathematical physics, and it quickly came to be perceived as unsolvable.

At the end of the 1930s, the invention of the electronic computer (first built with vacuum tubes, later with transistors and transistors on "chips") promised to transform the entire problem by making possible a large number of fast, accurate calculations. Better numerical approximation schemes (many of them rooted in the work needed to design and test the first nuclear weapons) became available. By the 1950s, people were seriously talking about making accurate weather predictions, not just for tomorrow or next week, but long-term, months or even years. Weather was one of the first non-military applications of these computers. Fantasies about controlling weather were floated as well, since accurate prediction and control are closely related.

Modern climate models, called atmosphere-ocean general circulation models (AOGCMs, or GCMs for short) have their roots in the postwar decades, the 1950s and 60s. They were put into their contemporary form in the 1980s and continue to serve as the main basis for the most complex long-term climate predictions.

And then chaos happened. Readers of this blog know what also happened during that period: the discovery of chaos by Edward Lorenz at MIT. By the early 70s, it was clear that long-term weather forecasting was doomed. A chasm opened up between hope and reality and between "weather forecasting" in the popular sense (limited to a week or two ahead) and "climate prediction" for the long term. Modelers retreated to a fuzzy distinction between "weather" and "climate," a distinction that has never been properly defined. Climate had to be defined statistically, as a set (or ensemble) or possible weathers, with some attached probabilities. Long-term predictions of climate would have to sample this ensemble, then average the results weighted by their respective probabilities. Because the full climate theory equations could not be solved accurately, heavy use of repetitive past weather situations to make future predictions came into play: in ordinary weather forecasting, known as synoptic meteorology; in "climate" prediction, as "climate parameterizations."**

Climate models: Successes and failures. The accuracy and control embodied in these GCMs are very uneven if we disaggregate the models into the various pieces that come from the fundamental theory. Before the next couple postings explain what's wrong with the models, it's a good idea to step back and point out what's right about them.

Mechanical equilibrium (pressure gradient balancing the pull of gravity downward) is the best-respected part of the whole standard climate picture. This piece gives us the pressure and density profiles as functions of altitude, as well as the atmospheric motions we know as winds. It's the thermal and chemical parts (heat transport and water phase transformations, respectively) where things get much hairier, because there is intermediate-scale structure smaller than the whole Earth but bigger than little parcels of air that are close to thermodynamic equilibrium: clouds, storms, cyclones, anti-cyclones, fronts.

Radiation and evaporation are the best controlled approximations in that sector of the models. Convection is under much poorer control, and turbulence essentially not at all. Neither are condensation and precipitation. "Global warming" due to infrared (IR)-opaque gases arises from the first two pieces (radiation, and the major enhancement of clear-air water vapor due to the much smaller effect of increased CO2 and CH4 concentrations). Not surprisingly, conventional climate models currently get these parts pretty well.

But the other parts, not under good control, are just as important. Convection is a significant heat transport mechanism in its own right and plays an essential role in getting water vapor above the bottom-most layer of the atmosphere to higher altitudes where it condenses into clouds. Turbulence embodies the chaotic, unpredictable evolution of climate. Condensation and precipitation complete the hydrologic cycle, form a major part of heat transport, and encompass the formation and dispersal of clouds. These in turn have crucial effects back on the radiation. Climate models don't get these parts well or at all. Not surprisingly, therefore, standard climate models overstate the degree of "global warming" due to IR-opaque gases: they get the warming parts, but do poorly with the anti-warming compensatory mechanisms, clouds above all.

The final two postings on climate models will drill further into these problems.
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* It was during this period that the Swedish physicist Arrhenius first noticed the effect of IR-opaque gases such as carbon dioxide (CO2) on the temperature lapse rate.

** In weather forecasting, if limited to no more than about two weeks ahead, synoptic techniques have a limited but real justification. The time horizon of prediction is short enough that chaos does not come into full play.

Escape from the greenhouse

What is a greenhouse? Is the Earth's climate a greenhouse? Why are infrared (IR)-opaque gases misnamed "greenhouse" gases?

What is a greenhouse? A greenhouse is an environment artificially controlled to maintain equable conditions of temperature and humidity suitable for growing plants in colder and highly variable climates. It's a controlled "climate box."

There is one source of heat in the Earth's lower atmosphere (visible and ultraviolet radiation incoming from the Sun) and three means by which the radiation, converted to infrared, can escape upward. In one case, it remains IR radiation and escapes as such. In the other two cases, convection and evaporation, the IR radiation is converted to a form of heat in matter (air and water vapor) before it moves upward. The first mechanism is, by itself, easy to understand and straightforward to control. The other two are much harder to either control or understand.

What a greenhouse does is to put a lid on the escape of heat through convection and evaporation. These two upward heat flows are trapped and turned back downward. OTOH, a greenhouse allows radiation in and radiation out unimpeded or only mildly controlled. Because radiation flow is easy to control, conditions in the greenhouse - temperature and humidity - can be regulated with a fair degree of accuracy. That's the point of a greenhouse. The walls of a greenhouse also put the kibosh on winds, shutting off another source of climate variability.

Is the Earth's climate a greenhouse? No. A greenhouse is close to a "pure radiative heat transport" situation. The Earth's climate is strongly influenced by the other two heat flow mechanisms and can't be considered a greenhouse, even as an approximation. Greenhouses are built because the Earth's climate conditions are not equable, especially in temperate regions that experience large daily and seasonal swings of temperature and humidity. The closest natural situation on Earth to a greenhouse is the tropics, and even there conditions vary a lot over the year. Upward heat convection and evaporation are, if anything, stronger in the tropics than elsewhere.*

But there's a deeper point. As concentrations of IR-opaque gases rise, they put a larger obstacle in the way of heat escaping from the surface as radiation, but they do nothing directly to affect the other heat flows (convection and evaporation). IR-opaque gases don't make the Earth's climate more "greenhouse-y" in fact. To do that would require strong limits on the other forms of heat transport, just as a real greenhouse does. But the IR-opaque gases modify the radiative heat flow - the opposite of a greenhouse.

Why the "greenhouse" effect and "greenhouse" gases? A posting last year discussed the origins of this misguided metaphor in both popular and scientific misunderstandings about heat transport from a century or more ago. In 1909, English scientist R. W. Wood proved that greenhouses don't "trap" radiation - quite the contrary.

Unfortunately, the bad metaphor stuck in decades of popular books and scientific texts on climate. Climate and weather books often flag the faulty double metaphor (greenhouses don't "trap" radiation, and the Earth's climate isn't a greenhouse anyway). But most scientists have given up on trying to fix it. Some books use other metaphors as catchphrases and mneumonics, like "atmosphere effect," for what is in fact a complex series of heat flow constrictions and diversions. Last year, I used the fairly exact analogy of a constricted garden hose.

The "greenhouse" and "greenhouse gas" language is fallacious through and through. Now that they have contributed to the rise of the "global warming" hysteria, these runaway bad metaphors have done far more damage than anyone could have imagined 50 or 100 years ago. The related bad metaphor of "heat trapping," rarely stated in explicit form, also lurks in the background and adds to the confusion.

A lesson from greenhouses about control and predictability. Armed with a correct understanding of greenhouses and why Earth's climate isn't one, we can see that greenhouses exemplify a very important point about control and prediction of climate.

Greenhouses have a steady climate inside because they're "radiation boxes." Radiation transport is the simplest part of the climate problem and, by itself, the easiest to predict. That's why greenhouses work: they rely on "radiation in-radiation out" only. Part of the trick of greenhouses is that they also shut off (or strictly confine) the other, "wilder" parts of climate, convection-turbulence and evaporation-condensation. If these forms of heat flow were allowed to roam wild and free, the temperature and humidity in the greenhouse could be not controlled or predicted. That would destroy its purpose and make the greenhouse no different from the general lack of predictability and control in the atmosphere - the real weather we face every day.

To paraphrase Foster Morrison again, the degree of isolation controls the degree of predictability. That's especially the case when climate has two parts wildness (chaotic-turbulent convection and evaporation-condensation) to one part easy (radiation). A greenhouse isolates a small piece of the atmosphere from the larger wildness outside and allows that piece to be heated and cooled by a steady and thoroughly nonchaotic flow of radiation.

The Earth's climate as a radiation box. It might be objected that viewed from the outside, the Earth's atmosphere is a radiation box. After all, there's no air or water vapor in outer space, so radiation is the whole game. Radiation flows in, and only radiation flows out. That's correct, but it doesn't make the Earth's atmosphere a greenhouse.

The ultimate reason is one of relative scales. In the Earth's atmosphere, the scale of convective heat transport is tens or hundreds of meters; the scale of evaporation and condensation (as clouds), a kilometer or so. The latter is six to 12 times smaller than the height of the lower atmosphere, the former 20 to 100 times smaller. There is no sense in which the Earth's atmosphere as a whole can be viewed as a single greenhouse - it's too big. It can fit many, many greenhouse-sized boxes. But none of these imaginary boxes would be closed; they would have to be open to air and water flows and thus not greenhouses. While they would have the right size, they would not function as greenhouses, which work because they isolate a small piece of atmosphere from the rest.

Without being closed to air and water flows, such imaginary would-be greenhouses couldn't act as greenhouses, with all their steadiness and predictability. And, because of its size, neither can the atmosphere as a whole.

POSTSCRIPT: Freeman Dyson, one of the last representatives still alive from the heroic mid-century era of physics, writes about "global warming," carbon dioxide, and plants in the New York Review of Books.
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* Thus the troposphere-upper atmosphere boundary is highest in the tropics, because of that strong upward "push." Upward convection and evaporation are weakest in the polar regions, and that same boundary is low over the poles, sometimes (during the polar winter) almost touching the surface ("sky falling to the ground").

Climate theory, models, and metaphors*

This and the next few postings cover a final technical examination of climate, a look at climate models, as promised earlier. A larger context is helpful too. Much of the lopsided and misguided debate on climate change is couched in terms of metaphors, necessarily fuzzy and usually linked to faulty analogies or models. Models in turn are frequently confused with climate theory, couched as integrodifferential and algebraic equations, the unique scientific truth about climate, but also unsolvable.

The full theory of climate contains:

• The mechanical dynamics of density, pressure, and wind;
• The nonequilibrium thermodynamics of heat transport in the forms of radiation, the hydrologic cycle (evaporation, condensation, and precipitation), and convection (often turbulent and thus chaotic);
• The nonequilibrium thermodynamics of water phase transformations; and
• In a more complete statement, other forms of chemical transport and transformation and the thermohydrodynamics of the oceans.

To be solved, the theory must be supplemented with initial conditions at some start time and spatial boundary conditions. The dynamical part of the theory alone needs a bunch of pages of graduate-level mathematics to state. The supplemental conditions require a detailed knowledge of atmosphere and oceans impossible to obtain, making the theory impossible even to state fully in practice.

Even if it could be fully stated, the dynamics itself cannot be solved. Suitably butchered, with the "hard parts" removed, parts of the theory can be solved, a fact that often misleads students (and not only students) into thinking that the full theory can be. Two properties of the heat and air transport and phase transformations render the problem intractable:

• Chaos, discussed extensively in a recent series of postings: exponential sensitivity to initial conditions, or, equivalently, essentially nonperiodic behavior.
  
  
• Discontinuity of water phase transformations, taking place in an infinitely complex pattern over the whole atmosphere and the atmosphere-land-ocean boundaries. These transformations affect the state of the matter (air and water mixture), but also affect the heat transport, being critical steps in the hydrologic cycle.

Approximations as rigorous method versus approximations as acts of desperation. When faced with such theories, the reaction of mathematical physicists and other quantitatively-oriented scientists is to substitute approximations of the full theory for the full theory itself, pick such approximations as are solvable, and attempt to justify the approximation.

All approximation methods aim at producing a tractable substitute for an unsolvable problem; their method is ranking different pieces of the problem in some order of "more important" (numerically bigger) and "less important" (numerically smaller). A starting approximation works with the most important pieces first; it can be refined and made more accurate by successively adding back in the less important pieces that were initially neglected. For this approach to lead to reliable results, there has to be a rigorous and controlled method for identifying, isolating, and ranking these pieces of the theory. As Foster Morrison puts it in his perceptive and useful Art of Modeling Dynamic Systems, the degree of precision is the degree of isolation: isolate one cause from another, one effect from another, one mathematical deduction from another.**

In mind-bogglingly complex problems like climate, there is no such method. Theorists make the leap anyway, just so they can get to something tractable. But in so doing, they are making only guesses of what's bigger and what's smaller. In some cases, partial justification can be found by appealing to observed climate behavior, which can (in favorable circumstances) hint that some things are more important than others. In other cases, the guesses are simply leaps in the dark, adopted for convenience, or suggested by historical precedent. And these considerations haven't even gotten us past the chaos problem. Only an infinitely detailed specification of climate at one instant of time, followed by an exact solution of the dynamics, can overcome this difficulty. We lack both, and so chaos limits, for example, weather forecasting to no more than two weeks ahead. Attempts to forecast for longer periods amount to guesses no better than random. We have to fall back on the notion of climate as a rough range, or a chaotic strange attractor. That attractor of behavior is a starting point for thinking about "climate" as something other than just "the infinitely complex instantaneous state of the atmosphere and oceans."

Theory replaced by models, and models reduced to often misleading metaphors. From a scientific point of view, accurate but unsolvable climate theory is, in practice, always replaced by solvable but uncontrolled climate models - models with limited usefulness, at best. From the point of view of the man in the street and the incessant chatter of environmentalists and the media, climate theory is a nonstarter. As a rule, in that context, we rarely rise even to the level of the simplest models and, if we think about it all, casually assume that such models are the last word on the subject - instead of a first and very preliminary word. More often, we're stuck swimming in an ocean of manufactured ignorance, pelted by a downpour of misleading metaphors.

A series of postings last year laid out these runaway bad metaphors and the climate model fallacies often implicit in them.

Fallacy #1. Radiative heat transport is the whole game, controlled by the concentration of infrared(IR)-opaque gases, such as water vapor, carbon dioxide (CO2), and methane (CH4).

But convection (including turbulence) and the cycle of evaporation, condensation, and precipitation also play a large role in Earth's climate. Radiation is not the whole game, and the heat transport is a complex three-way interplay of the water cycle, convection, and radiation, all acting alone and reacting off of one another. They all affect one another in a nonlinear and nonlocal way (nonlocal because radiation moves almost instantaneously through the clear air, in contrast to air and water.) As we'll see in the next few postings, the IPCC's predictions are based on enhanced CO2 concentrations (a small effect by itself), greatly amplified by the feedback of enhanced evaporation and clear-air water vapor. These typical and conventional climate models have a much harder time capturing convection, turbulence, condensation, and precipitation.

Once water evaporation is enhanced, no one knows how it will get divided between clear-air vapor and clouds. And clouds, as we know, have profound effects on climate, all cooling (lowering temperature).

Fallacy #2. The Earth's climate is a greenhouse. We'll look at this fallacy more closely in the next posting.

Fallacy #3. The obsession with temperature. Temperature, like pressure and humidity, is a local thermodynamic measurement. There is no "temperature of the Earth" - it's a whole temperature field distributed in space and changing in time. Confusions of this sort are shocking, not when committed by someone not educated in physics, but precisely by scientists and scientifically-educated nonscientists. Without the political hysteria, fallacies like this would be correctly viewed as laughable. Furthermore, even locally, temperature is not enough to specify the state of the atmosphere. You also need at least humidity and wind variables.

Fallacy #4. The confusion of temperature and heat. Temperature is not heat. They're even measured with different units, and they represent different physical phenomena. Heat is disorganized energy, disorganization itself measured by entropy. It's a "bulk" or extensive quantity: It can be localized, flow in space, and summed over volumes. Temperature is a local or intensive quantity. It measures how much of an increment of energy in a vanishingly small volume is related to an increment of disorganization or randomness (entropy) in that same volume. It's localized by its definition and doesn't flow in space or sum over volumes.

But even though they're not the same, there is an intimate relationship of heat and temperature. For a homogeneous system that does not suffer any discontinuous phase transformations (like melting or boiling), heat capacity relates how much a small increment of its temperature leads to a small increment of heat contained by it. If different parts of the system have different temperatures (like the climate), differences in temperature are closely related to flows of heat - the Second Law in action.

A system that does suffer discontinuous phase transformations - ice to liquid water, liquid to water vapor, and back - is altogether more complicated. A certain amount of heat, independent of changes in temperature, is needed to change ice to liquid water or liquid water to vapor. The same amount of heat is released by the opposite transformations. These heats of transformation, or latent heats, break the connection between increments of heat and increments of temperature. These heats, instead of raising temperatures, go into "loosening" the phase of the water - say, breaking up a tightly bound crystal of water molecules (ice) into a smooth fluid of water molecules that touch but slide past one another (liquid water). Our climate is a nonhomogeneous, nonequilibrium collection of flows suffering from just such discontinuous changes in water state.

Fallacy #5. It's heat that determines temperature. Actually, it should be clear by now, it's heat flow that determines temperature. The Earth's climate, from a thermal point of view, is an open system. Visible and ultraviolet radiation from the Sun flows in and is transformed into heat radiation, then flows back into space. Related fallacies include the "heat trapping" metaphor, as if the heat is locked in a closet and can't get out. IR-opaque gases don't trap heat; they change how it flows out.

Trapped in the greenhouse. The "greenhouse" metaphor (fallacy #2) itself is worth a closer look, not only because it's widely misused, but because a proper understanding of how a greenhouse works leads to a different, unexpected, and more accurate picture of climate and the relationship between controllability and predictability. We'll take a short and final detour through the greenhouse next.

MENTION MUST BE MADE of the passing of Edward Lorenz, the modern (re)discoverer of chaos, so tantalizingly anticipated by Poincaré. Twentieth-century science will be remembered for a handful of discoveries - the genetic code, the expansion of the universe - and for a few theories: relativity, quantum mechanics - and chaos. His original 1962 paper here (PDF).

Read more about Lorenz here, and consider his wonderful 1996 popular lectures, The Essence of Chaos.
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* This posting to an extent parallels Essex and McKitrick's chapter by the same name. (Their book is now available on the US Amazon.) I also make exceptionally heavy use of postings from last year.

** Morrison's book is a splendid introduction to dynamics for the mathematically-minded non-specialist. He starts without even calculus, managing a kind of "dynamics for the masses" by looking at compound interest, clocks, and thermostats.