Climate science blogs for you

From time to time, this blog will post links to blogs and Web sites devoted to climate science, climate change, and refuting the "global warming" hysteria. Here are a few.

One of the most influential and important is the blog of Steve McIntyre, who was and remains a key figure in exposing the fraud (not too strong a word) of the "hockey stick" - a horribly botched piece of junk science purporting to show that the world's "average temperature" (whatever that means) was stable until 1980 or so, when it suddenly started to increase at an accelerating rate. There were many fatal problems with the "hockey stick" (see here for a brief discussion of one of those problems), and McIntyre did yeoman work in exposing them. Unfortunately, the "hockey stick" lives on, like the Undead: it continues to serve as the centerpiece for the deeply flawed IPCC reports; it is the main basis of Al Gore's pathetic Inconvenient Truth; and it is the sole basis of those absurd "news" stories bleating about how "200x was the warmest year on record" (you fill in for "x"), in spite of the obvious cooling trend of the last few years (at least in the northern hemisphere). Incredibly, these "news" stories are based on faulty extrapolations of the original, faulty "hockey stick" - not the actual recorded temperatures for year 200x.

Another important Web site worth your time is the Canadian Natural Resources Stewardship Project, with their chief scientific advisor, climatologist Timothy Ball. Along with Canadians Essex and McKitrick (applied mathematician and economist, respectively), whose book Taken by Storm remains a classic deconstruction and refutation of climate change hysteria, our neighbors north of the border - like McIntyre - seem to have a corner on the climate sanity market. Blame Canada, I guess.

But not if Kavanna can help it! We're 100% Made in the USA =) .... as is the wonderful weather site of Intellicast. Intellicast's Dr. Dewpoint (remember dewpoint and saturation vapor pressure?) has published a series of clear and pithy online articles concerning climate change.

Saved by satellite radio?

Not so fast.

Those of us searching for better radio and a replacement for the degenerating broadcast radio industry have long been intrigued by satellite radio. You subscribe, and there are no ads - not even "sponsors" the way NPR has. Transmitted on much higher frequencies (shorter wavelengths) than broadcast AM and FM, satellite radio has bandwidth to burn and therefore huge potential for variety and satisfying every niche taste. The move towards a single technical standard, with inexpensive receivers installed in new cars, could make satellite, not broadcast, radio the new norm.

But alas, satellite radio has its enemies, in the form of the National Association of Broadcasters, a classic special interest group acting on behalf of existing broadcasters to attempt to squash improved radio via competition. And satellite radio has been hobbled by some of its own self-inflicted wounds. Radley Balko of Reason magazine reports.

Temperature lapsing

The last posting stated a set of imaginary climates, along with the real one, in terms of the temperatures of a few surfaces: the Earth's surface and the cloud tops and bottoms. The entities of the lower atmosphere are treated as a few idealized bodies, with temperature, pressure, and density varying by altitude, but not horizontally. Energy and heat flow in and out in a steady state. The biggest thing left out was the specifics of how temperature varies (and secondarily, pressure and density) with height above the surface, the lapse rate mentioned in an earlier posting. Refer back to the discussions of heat transport and condensation for a refresher.

Why is this variation important? Temperature differences signal heat flow, and in fact, heat flow determines temperature distribution. The specific relationship between how heat flows and how the temperature declines with altitude is all about the details of exactly how heat is transferred.

Bottom line up top: the dry adiabatic lapse rate of 9.8 ^oK/km is modified to a roughly constant 6.5 ^oK/km. Three of these modifications, the non-adiabatic radiative and convective heat flows and the removal of water vapor pressure by condensation, steepen the lapse rate. The fourth, the saturation-adiabatic injection of latent heat, strongly moderates the lapse rate, making it shallower. It is the latent-heat release moderation that wins, at all altitudes in the troposphere. The temperature at the tropopause is a frigid 217 ^oK = -56 ^oC = -69 ^oF, but not as frigid as it would be if the lapse rate were steeper than it actually is.

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Start with local thermodynamic equilibrium (LTE), which includes mechanical, thermal, and phase equilibrium, supplemented by steady inflows and outflows of radiation and evaporative heat. The real atmosphere is not this, but it never strays far from it. Global equilibrium is violated by the energy flows and by the fact that pressure, temperature, and phase of water vary with altitude. The pressure (mechanical) equilibrium is the closest to exact. Hydrostatic equilibrium (relating the pressure lapse rate to the density and gravitational acceleration) is almost exact at all times and places, except in severe weather like tornadoes.

If we ignore energy flows, the atmosphere is adiabatic, which just means no heat is being added from or released to the outside. The dry adiabatic lapse rate is 9.8 ^oK/km = 5.4 ^oF per 1000 feet, the gravitational acceleration (g = 9.8 m/s²) divided by the heat capacity of dry air at constant pressure (cP = 1004 J/kg·^oK). With a small, realistic addition of water vapor, the heat capacity is slightly raised, and the wet adiabatic lapse rate reduces slightly to 9.7 ^oK/km.

Allowing water vapor to condense into liquid droplets (usually visible as clouds) and phase equilibrium to be established completes the LTE picture, but it also complicates the vertical temperature slope. Schematically, it now looks like:

           g     [1 + vapor-pressure-decrease]
dT/dz = - --- * -------------------------------
         cP           [1 + latent-heat]

This saturation adiabatic lapse rate is not constant with altitude z, but varies from about 4.7 ^oK/km to a steeper 6 or 7 ^oK/km at higher altitudes. The actual lapse rate averages over the whole troposphere to 6.5 ^oK/km, although it varies significantly with time of day, season, and whether or not clouds are present. Why is the lapse rate fairly constant with altitude?

Two critical components are missing from the adiabatic lapse picture, both the effect of radiative and convective heat flows. These flows violate thermal equilibrium,* which is less respected than hydrostatic equilibrium: the real atmosphere is not adiabatic, because heat is continually flowing in and out, at a roughly steady rate. The lapse rate now schematically looks like:

           g     [1 + vapor-pressure-decrease + rad + conv]
dT/dz = - --- * --------------------------------------------
         cP               [1 + latent-heat]

The rad and conv terms, by themselves, tend to steepen the lapse rate. But their effect has to be gauged together with the other terms to see the complete result in dT/dz. Each term is proportional to the heat flowing by that mechanism, radiative or convective. Their presence steepens the slope of T because more heat flowing implies bigger temperature differences.

Although it is less important in the clear air and harder to understand theoretically, start with convection. In this mechanism, parcels of overheated wet air move up, dump their heat at a higher altitude, then float back down - like a waterwheel. There's no net motion of air, just as a waterwheel suffers no net motion; but there is a net flow of heat from lower to higher altitudes. The average convective motion of heat in the clear air well away from the ground is slow, less than a meter per second. The convective mixing length is roughly 20 to 30 meters. Clear-air convection is fairly turbulent and inefficient: in clear air, those overheated parcels tend to lose their heat quickly. In clouds, the mixing length doesn't change much, but the convective velocity roughly triples. Cloud convection is much more efficient, because clouds are opaque: the convective parcels keep their heat until they reach the cloudtops. The conv term in the temperature lapse rate is proportional to the product of the convective velocity and mixing length.

Radiative heat transfer in clear air is diffusive: infrared (IR) or heat photons are absorbed and re-emitted by air molecules many times before they reach the top of the troposphere. Only certain molecules are really good at this, the main one being water vapor. (Oxygen and nitrogen, OTOH, don't do much with photons of that wavelength - about 5-20 microns or millionth of a meter - about 10-40 times the wavelength of visible light.) Any matter that's really good at absorbing radiation at particular wavelength is also good at emitting it.** IR-sensitive molecules like water vapor don't absorb and hold heat; rather, they're exceptionally efficient at passing the heat along. Adding more water vapor to the clear air, for example, makes the rad term in dT/dz larger, steepening the lapse rate, and speeding up heat flow.

In clouds, radiative heat transport is ineffective, and convection takes over the whole burden of transporting heat upwards to the cloudtops. That's why the convective heat transfer velocity jumps considerably in clouds.

The curious thing is that in the lower atmosphere, these factors that control how fast temperature drops all harmonize to make that rate remain close to -6.5 ^oK/km. Much of the explanation rests with the magical properties of water, both vapor and liquid droplets.

Low altitude, clear air: The radiative term rad is at its largest here, because the water vapor is densest near the surface, its source. But the condensation-driven latent-heat and vapor-pressure-drop terms also have their biggest effects here, and the two effects compete. The condensation effect wins out, keeping the lapse rate shallower than the dry adiabatic value of 9.8 ^oK/km. The convective term conv is small but significant.

Higher altitude, clear air: The rad term fades in significance. The conv term is about the same. The condensation-driven terms also get smaller.

Clouds: The condensation-driven terms continue to shrink. (That might seem strange, since clouds are the most visible result of condensation, but we're looking at the heat transfer, not the reflection of visible light that our eyes can see.) The rad term disappears, while the conv term increases and roughly compensates for the loss of rad.

Above the clouds: The amount of water vapor (or crystallized ice) is much smaller now than it was below. The rad term returns, smaller. The condensation terms are smaller but still significant. The conv term is smaller than in clouds and stops altogether at the tropopause, because the temperature stops lapsing at that point.

As the previous posting explained, isolating different mechanisms at work is important to sorting out the physics of climate. But in reality, adding or removing water from the atmosphere is a single-step thing: it has all of those ramifications (radiative, vapor pressure, latent heat) simultaneously. The distinction among the different effects of water in the air is conceptual and verbal, not physical.
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* The final component of LTE is phase equilibrium, which of the three components, is the most routinely violated in a fairly obvious way by the formation of clouds (through evaporation followed by condensation), the dissipation of clouds by precipitation or evaporation aloft, and by heat flows. LTE allows clouds to have condensed, but not to be condensing; and liquid water to have evaporated but not to be evaporating. OTOH, it is precisely in stable clouds that LTE is most respected: there is a good approximation to phase equilibrium between water vapor and liquid droplets.

** More exactly, at any particular wavelength of radiation, the radiative absorptivity of matter = radiative emissivity of matter, Kirchhoff's law of radiation. You might remember Kirchhoff from his two laws of electrical circuit analysis (which are just energy and charge conservation in a restricted form). Same brilliant Kirchhoff, different branch of physics.

Heat in the troposphere: Putting it all together

The thermodynamics of the lower atmosphere, including all the phenomena of weather, is shaped decisively by the Earth. Its gravity, in balance with air pressure, determines the way temperature, pressure, and density drop with altitude, all the way to outer space. The lower atmosphere is primarily heated from below, by visible and ultraviolet (UV) radiation absorbed from the Sun and re-released in various forms we'll discuss presently. That's one way to define what's meant by "lower atmosphere." Another, more descriptive way is captured by the name "troposphere," from the Greek tropein, "to turn over." It runs from the Earth's surface to the tropopause, at about 11 km altitude.

The lower atmosphere is where convection, evaporation, and condensation happen. They're important enough to significantly augment and alter the heat flow. And how heat flow is distributed is how temperature is determined. Heat flows from higher temperature to lower. But in a system not in thermodynamic equilibrium (without a single temperature and pressure), higher and lower temperatures are better thought of as being caused by pre-existing heat flows, rather than vice versa.

To understand the temperature distribution of the troposphere, keep in mind two principles:

• It's best to understand the temperature of distinct entities first (in this case, the Earth's surface, the lower atmosphere, and the clouds); then secondarily, understand the vertical temperature profile as a continuum (that will come in the next posting).
  
• If the atmosphere is a steady state (and it's never far from that), energy conservation can be applied to any entity you can draw a boundary around. For the climate, that means a balance of power flows for such entities: power in = power out.
  

There are three ways to apply power balance. For the surface by itself:

• solar radiant power in (what isn't reflected or absorbed by the clouds) + heat emitted down by clouds + heat needed for evaporation = Earth heat radiated upward + Earth heat convected upward + net latent heat released by evaporation-condensation

For the lower atmosphere + surface as a whole:

• solar radiant power in (what isn't reflected by the cloudtops) + latent heat in = heat radiated out from the surface under clear skies + heat radiated out from the cloudtops

For the clouds, treated as a single cloud deck:

• solar radiant power absorbed (what isn't reflected and what isn't transmitted through) + Earth heat radiated upward + Earth heat convected upward = heat radiated up from the clouds + heat radiated down from the clouds

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Now imagine a series of increasingly realistic Earth atmospheres, starting with an airless, waterless Earth. Although the Kelvin and Celsius scales have different zeros, their temperature increments are the same. The values here should be taken as representative of the temperate zone during spring or fall. In the actual atmosphere, the values vary quite a lot by latitude, season, time of day, and whether you're over land or water.

Airless, waterless Earth: T(surface) = 279 ^oK = 6 ^oC = 43 ^oF. The surface temperature is determined solely by the absorption and re-emission of solar radiation by the surface. The cases of dry air and wet air, with free water vapor only: same surface temperature.

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Now let's get more realistic with the water. Allow it to condense as required by the law of water vapor saturation (but don't make clouds yet). Evaporation and condensation also inject an additional and continuing flow of heat into the air equivalent to about 22% of the total incoming solar radiation.

Wet air with heat injected by evaporation-condensation cycle: T(surface) = 304 ^oK = 31 ^oC = 89 ^oF.

Notice how hot the climate would be, not to mention humid. There are no clouds yet to block out the Sun, cool things off, and lower the evaporation rate. So let's add clouds, but not real ones. Instead, just add ultrathin clouds that reflect, but do nothing else - no absorption or re-emission of radiation and no internal convection. We'll add the cloud cover that our real Earth has.*

Wet air, evaporation, condensation, and clouds that only reflect: T(surface) = 269 ^oK = -4 ^oC = 25 ^oF. The clouds themselves have temperature T(clouds) = 226 ^oK = -47 ^oC = -53 ^oF. Brrr! Now it's pretty cold at the surface. Why isn't the Earth this cold? It's not because of convection. If we add that, the cloud temperature changes, but not the surface temperature.

Add clear air convection: T(surface) = 269 ^oK as before. But now T(clouds) = 247 ^oK = -26 ^oC = -15 ^oF.

Finally, add the last missing element: realistic clouds, with real thickness, internal convection, and above all, capable of absorbing and re-emitting radiation in their own right. Real clouds are as important radiators as the surface itself.

Add real clouds: T(surface) = 288 ^oK = 15 ^oC = 59 ^oF. Up in the sky, T(cloud bottoms) = 275 ^oK = 2 ^oC = 36 ^oF and T(cloud tops) = 250 ^oK = -23 ^oC = -9 ^oF. This is climate as we know it.

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Here's another purely thought-experiment way of slicing up the climate. Imagine we had started with clouds that only reflect and only solar radiation as energy input flow, with no evaporation. This is obviously not realistic, but it forms as important, often-quoted, and sometimes misleading baseline to gauge the overall effect of the "damp and shiny-on-the-outside cloudy blanket-steambath." In that case, we would have: T(surface) = 250 ^oK = -23 ^oC = -9 ^oF, as well as T(clouds) = 210 ^oK = -63 ^oC = -81 ^oF. Again - brrr!

But now add evaporation and recover: T(surface) = 269 ^oK = -4 ^oC = 25 ^oF and T(clouds) = 226 ^oK = -47 ^oC = -53 ^oF. Finally, add real clouds again and recover the real climate: T(surface) = 288 ^oK = 15 ^oC = 59 ^oF, with T(cloud bottoms) = 275 ^oK = 2 ^oC = 36 ^oF and T(cloud tops) = 250 ^oK = -23 ^oC = -9 ^oF.

The actual surface temperature is 288 ^oK. The temperature enhancement due to water in the lower atmosphere is often quoted as this +38 ^oK. Of that total, +20 ^oK is due to evaporation, and +18 ^oK is due to having real clouds (as opposed to the fake, ultrathin but shiny clouds).

Why do climatologists and meteorologists think of the lower atmosphere in this way? It isolates temperature enhancements due to everything except the incoming solar radiation. By drawing up the heat flow "budget" in this way, we can see the enhancement of temperature by the rerouting and augmentation of heat flows in the lower atmosphere.

One striking result emerges from this approach: the actual cloudtop temperature is what the surface temperature would have been in this imaginary scenario. And the imaginary cloud temperature is close to the actual temperature at the tropopause, something to be explored in an upcoming posting. It's almost as if the imaginary climate constructed here is one in which "the sky has fallen to the ground." The polar regions during polar winter are as close to this scenario as can actually be achieved on our planet: almost no clouds, and virtually no convection.

But there's also a price for looking at climate this way: it's physically unreal. There are no clouds with zero thickness that reflect but don't absorb or radiate. And there are no clouds without evaporation of surface liquid water to support them. If we're thinking about how the climate might change with modification, addition, or subtraction of its components (air, water, radiation) or heat transport mechanisms (radiation, evaporation, convection), we have to take into account all the consequences of any hypothetical change. Failure to do this leads to faulty reasoning and wrong conclusions. This imaginary 250-^oK climate is a mathematical fiction designed to isolate the effect of certain modifications of heat flow. No real climate could look like this.**

Of course, it's hard to trace out the consequences of real or imagined changes to basic climate inputs. For the purely radiative part, it isn't impossible. For the evaporative part, it's harder; and for convection, essentially impossible, at least to the accuracy needed for weather forecasting. This has serious consequences for attempts at long-term prediction - or for claims to have already made such predictions.
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* Mean cloudiness is 0.54.

** Of the hypothetical alternative climates listed here, only one has any chance of being close to realizable: the no-cloud, evaporation-only climate with T(surface) = 304 ^oK = 31 ^oC = 89 ^oF. And a strange world it would be: mostly ice-free, hot, humid, but with few clouds - it would rain frequently in mini-showers, so clouds wouldn't persist. But wait - the Earth's climate not so long ago was sort of like that. We'll have reason to return to this point later.

The private equity revolution

Everybody's talking about it: the revolution of "going private" in U.S. business. It means publicly traded companies buying back their stock shares, or always-private companies never "going public" - starting to sell shares of ownership - in the first place. Why is it happening, and what does it mean?

There's always been a quiet countercurrent of private equity in American capitalism throughout the last century, which was loudly dominated by the publicly-traded stock revolution. Precisely because they're not publicly traded, you see and hear little in the conventional media about private companies. The big immediate stimulus to the current "counterrevolution" is the overburden of reporting requirements imposed on public companies by the Sarbanes-Oxley ("Sarbox") Act of 2002. The Sarbox law was passed in the wake of major scandal fallout from the excesses of the late 1990s. The most extreme and best-known of these corporate governance scandals - squandering and stealing investors' money, essentially - were those of WorldCom and Enron. Sarbox is classic political overreaction stimulated by saturation media coverage. It requires something analogous to everyone in the country filling out a stack of forms every three months to certify that they're not axe-murderers - after a few years of saturation coverage of Lizzie Borden made everyone hyperconscious of axe-murdering. The forgotten truth is that what the managers of WorldCom and Enron did before 2002 was already illegal many times over, and all of them are suffering various punishments on that basis.

The private equity revolution is investors' own reaction to the negatives of publicly-traded stock, separate from and in addition to the better-known regulatory reaction. And a surprising fallout from the new Democratic majority in Congress is that serious reform of Sarbox might be in the offing.

We take public equity for granted today, but in the long view of history, it's a strange institution that fits the realities of ownership and management poorly. Adam Smith, in the Wealth of Nations, firmly concluded then (in 1775) that separation of ownership and management of an enterprise was impractical. It exposes owners (investors) to the risk of having their investment mismanaged by other people (managers) who have shaky incentives to make proper use of investment money. In good times, investors would tend to lose interest and awareness of what was happening with the company they invested in. Managers would have an incentive to line their pockets and play fast and loose - it's not their money, after all. Smith didn't know about the modern media, but he would have quickly grasped the further bad side effects of anonymous public investment markets stemming from a investment public with limited knowledge and interest inundated with irrelevant or misleading information.

And so public equity remained virtually unknown until the middle of the 19th century. The emergence of national- and international-scale economies in the second third of the 19th century, with technological revolutions in communication and transportation, changed that. Large companies got much larger and required previously-unheard-of mounds of capital for their operation. No small group of owners could provide savings on this scale, and so modern equity markets were born. A useful date in this evolution to remember is the founding of the Dow Jones Company, parent company of the Wall Street Journal and Barron's, in 1882. From the start, modern equity markets were vulnerable to the problems Smith predicted. Periodically - at the turn of the century, in the 1920s, in the 1960s, then against in 1980s and 1990s - investment bubbles would appear and then burst, with serious consequences. A new type of scandal emerged - the corporate scandal - where managers would do something wrong, either by mistake or by design, with investors' money not their own. The major counterforces to these tendencies have been the growth of business reporting and the rise of governmental regulation. Both are good things - up to a point.

There's another factor that separation of ownership and management brought into play, one that Smith also anticipated, and that is the refocusing of corporate energy and attention on investors and away from both employees and customers. Many of the problems with modern corporations stem from this condition. The point of being in business is to provide customers with goods and services. (The point is not making a profit; that's just the reward, and also an indicator of doing something right.) Much of the lopsidedness of modern corporations - the practically instant creation of small groups of big winners in IPOs and overpaid executives - stems from their relationship to investment markets, not to customers. A company focused on customers tends to have power and responsibility spread throughout the organization. A company focused on investors tends to have power concentrated with the people who have control over the issuing of stock and debt and the privilege of frequent media attention.

Is the private equity revolution a good thing? Probably. The technology is there for small-scale enterprises to manage large amounts of information. But the main reason for small business failure is and has always been undercapitalization. So the question lingers: can privately-held companies generate the capital they need to stay in business and expand?

Radiation, conduction, convection, evaporation: A précis

Sometimes all these mechanisms for transferring heat get a little complicated and hard to remember. So time for a time out, to explain each in turn, how they're similar and how they differ. Some homey examples and analogies should help too.

First, what heat is: it's disorganized energy, disorganized at the molecular or microscopic level. It represents entropy, a quantitative measure of disorder. In thermodynamics, heat is usually contrasted with work, which is energy organized at the "large" or macroscopic level. Both are measured in a common energy unit, the joule. In the old days, heat was measured separately in calories, but for various good reasons, all forms of energy are quoted today (at least by physicists and more and more by chemists) in a common unit. A calorie is about 4.2 joules.

Temperature is a measure of how disorganized the energy of a system is. When a system is at thermal equilibrium - that is, its energy is as disorganized as it can be - temperature is a measure of the "typical" energy distributed to each tiny microscopic degree of freedom, each independent motion the system's microscopic components can execute. In equilibrium, by its nature, the average energy of each degree of freedom is the same. If the system is not in such a state, it's not in thermal equilibrium. In such cases, it's often possible to assign a different temperature to each subsystem, suitably defined, and the system is said to respect local thermal equilibrium (LTE for short - that is, not global - such a system has no single temperature). The Second Law of thermodynamics tells us that varying temperatures imply heat flows from higher to lower temperatures. In the real world, it's best to think of heat flows as fundamental and the variable temperature distribution as an effect, not a cause.

The Second Law also implies that such heat flows act to move the system in the direction of greater entropy and thus "towards equilibrium." All the Second Law requires is that a system not in equilibrium move "toward equilibrium." It doesn't specify the mechanism of entropy increase, or how fast the movement is, or that the system ever reach equilibrium. Those are the details that depend on the exact nature of a system's constituents and forces.

The three standard mechanisms of heat transport - conduction, convection, and radiation - all move heat from higher to lower temperature and generate increasing entropy along the way.* So does evaporation-condensation - it's often lumped together with either conduction or convection, but it's helpful to separate it out as a fourth, distinct mechanism in its own right. Depending on the exact details, one mechanism is more or less efficient than the others; the most efficient mechanisms dominate the heat flow. (The most efficient are the ones that generate the least entropy for moving a given amount of heat.)

The different mechanisms can be divided or contrasted in at least three ways, and these distinctions help to define the them.

1. The most fundamental distinction is the medium of transfer. Heat can be the disorganized motions of matter particles (molecules). The molecules themselves don't have to move far or, on average, move at all, to transfer heat to their neighbors by collisions. Or they can execute organized, coordinated motion. Conduction, convection, and evaporation-condensation all fall into this category.

The other disorganized particles that can carry heat are photons, the particles of radiation.

2. Some heat transfer moves heat in more or less straight lines, which is pretty efficient. Convection always works this way. Evaporation-condensation, if combined with convection, also moves in straight lines. Liquid water absorbs enough heat to convert to vapor, moves as an organized mass somewhere else, then condenses and dumps that heat at that somewhere else. Radiation can as well, if it moves through a material medium transparent enough to not pose much of a barrier.

The opposite of straight-line transfer is diffusion. Molecules bang into one another, or photons get batted from one molecule to another, in an almost random way. I say almost random, because it isn't quite! The system isn't in thermal equilibrium (remember: heat is flowing), so there's a slight bias. On average, the more energetic molecules transfer heat in the direction of lower temperature (or the more energetic photons move that way). But there's a lot of jostling around along the way. As you might imagine, it's generally a less efficient way to move heat. In matter, heat transfer by diffusion is called conduction. It's common, depending on the density of material. And radiation can also diffuse, if it's moving through a material medium absorptive (opaque) enough that it can't move in a straight line. Instead, photons are absorbed and re-emitted multiple times before their heat gets across the medium. The plasma of a star's interior is the classic home of radiative diffusion, as was the early Big Bang. For infrared radiation, the wet air that appears transparent to us poses a partly opaque barrier that can only be traversed by diffusion.

3. The third great division is between heat transfer mechanisms that require phase changes in matter and those that don't. A phase change is like the change of liquid to vapor, or ice to liquid. It's a qualitative change in how the molecules are organized, from one state of matter to another.

Evaporation-condensation is obviously such a mechanism; it needs two phase changes to work, one to absorb the heat somewhere, the other to dump it back somewhere else. Evaporated water molecules can get from somewhere to somewhere else by diffusion or by convection. In real life, it's by some mix of the two.

A more difficult fact to appreciate is that convection itself also requires a phase change. Without convection, there's no large-scale, organized flow of heat. Under the right conditions, convection "switches on," and matter parcels, eddies, or "blobs" that are overheated relative to their surroundings move the excess heat from their origins to their destinations, where they give up the excess heat and lose their identities as distinct "blobs." The phase change here is from a state of "no macroscopic motion" to a state of "macroscopic motion."

Why does convection happen at all? And where does it happen? Convection might seem counterintuitive in light of the Second Law. After all, if a system is supposed to get more disorganized over time, how can it switch to a coordinated, macroscopic movement of overheated blobs? The answer is that such movements don't violate the Second Law; they fulfill both its letter and spirit in a subtle way.

Convection requires work to move the overheated parcels from one place to another, if that motion has to overcome friction, gravity, or other forces that otherwise would hold them in place. That work has to come from stored heat, in apparent violation of the Second Law. But - if the blob is overheated enough compared to the temperature of where it's going, by dumping its heat in the cooler location, it can increase the total entropy, which is all that matters for the Second Law. The decrease in entropy needed to convert disorganized heat into organized work is more than compensated by the increase in entropy once the heat gets to the cooler place where it's going. By Second Law accounting, convection "pays" in such cases, so to speak. There's an exact formulation of this condition, called the Schwarzschild criterion, that decides when and where convection switches on.**

We're familiar with this in everyday life. If you heat a pan of water on the stove, you can get heat currents going only if the temperature contrast between the bottom layer of water and the layers above is big enough. Then it starts to boil, and you actually see the blobs of overheated water rising (often with air bubbles carried along), doing work against gravity, but also transferring heat upwards to the cooler layers. The same thing happens in the atmosphere and especially in clouds. The distance over which the blobs retain their distinct identity as overheated relative to their surroundings is called the convective mixing length.

Except for very smooth convective flows, convection in fluids is turbulent, a concept that has an exact meaning we'll learn about later. That makes it very hard to understand in detail. Turbulence is actually a larger phemenon in the atmosphere that encompasses a wide spectrum of spatial sizes and velocity scales. Convective heat flow is just one slice of turbulence, with overheated blobs of a certain size moving within a certain range of speeds. The full theory of convective fluid flow is impossible to solve, so physicists and engineers use approximations, some better than others, but none really accurate in all situations. And while evaporation-condensation by itself is fairly simple, the combination of evaporation-convection-condensation is really hard, even more difficult than convection alone.

Heat transfer in the atmosphere. The air is too thin for conduction, or matter heat diffusion, to be important. Radiation is the main way heat is transported in the lower atmosphere and the exclusive mechanism in the upper atmosphere. For the infrared type of radiation the Earth emits from its surface, the atmosphere is fairly opaque and the heat transfer mildly diffusive.

But in the lower atmosphere, convection and evaporation-condensation also play important secondary roles. In clouds, which are so opaque that radiative transfer is suppressed, condensation and convection are the whole show. Anyone who's flown in a small plane through thick clouds has experienced this fact first hand.

Heat transfer in the oceans and underground. Conduction is important here and actually the main mechanism. Convection does play an important role in the oceans, however, and even in the solid Earth, where plumes of heat from the core rise to the surface and appear as geysers, volcanoes, etc.
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* How much entropy? The increment (differential) of entropy is dS = dQ/T, where dQ is the increment of heat. (That relation defines temperature.) The net entropy created by moving the same amount of heat dQ from higher temperature T₁ to lower T₂ is dS = dQ₁/T₁ + dQ₂/T₂, where -dQ₁ = dQ₂ = dQ > 0 is the amount of heat released at T₁ and absorbed at T₂. The Second Law requires T₂ <>1, so dS = dQ*(1/T₂ - 1/T₁) > 0. That is, the total entropy increases on net. This is the Second Law in quantitative form.

** If you've read about black holes, you've surely heard of Schwarzschild, a slightly older contemporary of Einstein. Same brilliant Schwarzschild, different branch of physics.

Condensation, clouds, and the rain in Spain

Temperature change (slope or gradient) is determined by how heat flows in matter. The fall of temperature with altitude (the lapse rate) is determined by a combination of gravity, the heat capacity of air, the condensation of water vapor, how heat is convected upward by overheated air parcels, and how heat (infrared) photons diffuse through water vapor. This posting talks about the first three factors and touches on the fourth. Air pressure and density also drop with altitude, in a more complicated way related to the way temperature drops.

For heat, I use the universal unit of energy, the joule = newton times meter. A newton (N) is a unit of force and equals a kilogram-meter per second squared. Quantity of heat sometimes quoted in calories; the equivalence of heat and mechanical energy is 4.1860 joules (J) = 1 calorie (cal). Physicists and chemists no longer use the calorie except when relaxing with friends. Its definition depends on the heat capacity of liquid water, which depends slightly on temperature - not good if you want a simple, stable unit.* A more familiar unit is the watt (W) for power; one joule is one watt-second.

For dry air, with no water vapor, the lapse rate is 9.8 ^oK per kilometer = 5.4 ^oF per 1000 feet. The lapse rate is just the gravitational acceleration (9.8 m/s²) divided by the heat capacity of dry air at constant pressure (1004 J/kg·^oK).

The temperature falls with altitude because the air, in order to rise, has to do work against gravity. The work comes from stored heat. The heat stored in dry air is proportional to temperature, while the work done is proportional to altitude and is in fact converted to gravitational potential energy. So the temperature falls linearly with height. The rise of air in a dry atmosphere is very slow or quasi-static (adiabatic). It takes weeks or months for atmospheric heat to be fully distributed. This feature causes the lag of seasons: the coldest period of winter is 4 to 6 weeks after winter solistice; the hottest period of summer is 4 to 6 weeks after summer solistice. Similarly, the hottest hour of the day is around 2 pm, not noon.

For wet air, with water vapor but no condensation, the lapse rate is 9.7 ^oK/km, slightly lower. The heat capacity of air at constant pressure with a little water mixed in is a little larger than that of dry air.**

The saturation pressure of water vapor drops with altitude, as the temperature drops. At higher and higher altitudes, more and more of the water vapor condenses to liquid water. As it does so, it releases the latent heat or heat of condensation, just the reverse of the heat of evaporation that got the liquid water into vapor in the first place. The heat of condensation is about 2.5 million joules per kilogram of water.***

For wet air, with increasing condensation of water vapor with altitude, the lapse rate becomes more complicated. A "typical" value representative of temperate zone climate near the surface is 4.7 ^oK/km. This value excludes the effect of heat transport by radiation diffusing through wet air and so is not appropriate for clear air. It is for a cloud; but clouds (except fog, which is just a cloud at the ground) reside at higher altitudes, and the lapse rate there runs between 6 and 7 ^oK/km. Inside a cloud, heat has to be transported by convection alone, since the inside of a cloud is opaque to radiation.

Notice how much smaller the lapse rate is with floating condensed water. That's the effect of the released heat of condensation, and it answers the question, "How much does condensed water vapor heat up the lower atmosphere?" The temperature still drops with altitude, but not as fast as without condensed water.

Condensation, clouds, and precipitation. Not all condensed water droplets in the air conglomerate into clouds. Condensation is happening all the time above our heads, but only some of the droplets form clouds, and even fewer of the droplets come down as precipitation. Clouds are made up of larger droplets, which require some particles to form around, like suspended dust. If the particles are man-made pollutant particles, the cloud is called smog, a mix of smoke and fog. Only if the droplets grow to quite large sizes (millimeter or more) do they weigh enough to come down. That typically requires, not just condensation, but crystallization into ice at high altitudes. Otherwise, air updrafts (upward convection) keep them floating above.

The upward transport of heat by water evaporation at the surface and condensation aloft, followed by precipitation, is the Earth's hydrologic cycle. It is secondary to radiation as a form of heat transfer in the lower atmosphere, but still very important. It's about one-seventh of the total heat flow upward from the surface. (Released latent heat and convection together are about one-fifth.)****

Clouds play another and even more important role we'll learn about next. They act as absorbers and emitters of heat radiation in their own right. At the same time, their internal convective heat transport is very efficient, constituting a significant enhancement in cooling the lower atmosphere. Convection in the clear air is far less efficient. These factors are crucial in explaining the lower atmosphere's enhanced temperatures, in addition to the heat released by condensation.
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* Note to dieters! What's called in nutrition and medical circles a "calorie" is really a kilocalorie - a thousand times a real calorie.

** Water mixing ratio by mass = 0.006, corresponding to one water molecule for every hundred molecules of air. The mean molecular weight of wet air is 28.9; that of water is 18.

*** An intense workout at the gym, say, 500 "calories" = 500,000 calories = 2.1 million joules, is almost enough to convert one kilogram of liquid water to vapor. Next time you're at the gym, think about how much water you lose as vapor instead of sweat.

**** Throw around phrases like "condensation aloft" and "adiabatic lapse rate" long enough, and you'll start to sound like a real meteorologist :=)

Holocaust in mind

Today is Yom HaShoah, remembrance day for the victims of the Holocaust.

In December, a very large, previously restricted archive of Holocaust-related material was opened to the public, at the German town of Bad Arolsen. It was collected by the Red Cross at the end of the war from materials captured by Allied forces or turned over by German officials. It contains over 50 million pages of documents on all aspects of the Nazi genocide, including, but not limited to, its six million Jewish victims. It covers others subjected to enslavement and mass murder as well - certain Slavic nations (Poles and Serbs), Russian POWs, and Gypsies, among others. The mechanics of genocide are preserved with unnerving and sometimes bizarre thoroughness.

In December, the CBS news magazine 60 Minutes carried this 13-minute segment on the archive. The main article is here.

Atmospheric heat: What gets in, what gets out, what stays

The Earth's atmosphere is continually changing. Its temperature distribution is really a snapshot of a continual flow of radiant energy in from the Sun and out from the Earth. How heat flow is distributed is how temperature is determined.

Heat can not only flow by different mechanisms (convection and radiation in the air, conduction and convection in the water and ground), its flow can be split up by different parts of the atmosphere and Earth so that different parts "capture" different amounts of heat at different efficiencies. Extra flows, not directly driven by the Sun, appear as well that remain solely in the lower atmosphere and modify its temperature distribution. The simple picture of solar radiation absorbed and re-emitted is too simple. How heat is captured, concentrated, and moved around in the lower atmosphere is not the same question as how solar energy gets in as light, then escapes as heat, although the two questions are intertwined.

The mean solar radiant energy flux at the Earth's orbit is about 1370 watts per square meter. Because only half the Earth is facing the Sun and the Earth is a sphere, not a disk, geometric factors reduce the effective input by a factor of four, to about 342.5 watts per square meter. About 65% of the Sun's incoming light makes it into the lower atmosphere. Clouds reflect 35% back into space and absorb another 19%.* The 65 - 19% = 46% that remains is absorbed by the Earth's surface. The Earth re-releases that 46% energy flow as infrared radiation, upward convection, and latent heat of water vapor. (The Earth also absorbs another flow of heat directly from the air near the surface that helps to evaporate the water.) The clouds re-emit their 19% share as radiation as well, both upward and downward. The radiative part of this flow is fairly easy to understand. The convection and evaporation part is much harder. That 65% of the total incoming must flow at the same rate back into space. It mostly flows upward by radiation, some by convection; and, once it gets to the upper atmosphere, all by radiation. But pieces of that flow are diverted and re-routed in the lower atmosphere. And the lower atmosphere's air and water are not in complete equilibrium, even locally. Water vapor, condensed water, and air all have somewhat different temperatures.** Water vapor and condensed water droplets are not in chemical (phase) equilibrium, except at saturation (that is, in clouds).

If the Sun were "turned off" and then suddenly "switched on," a very cold Earth would heat up, very gradually, over months, until the radiant energy flow in = radiant energy flow out. This "steady state" (misleadingly called "radiative equilibrium" sometimes) is the foundation of understanding the Earth's climate. Many weather books refer to it as the Earth's "heat balance." It's not really an exact steady state either; rather, it varies over a small range. Sometimes the Earth takes in a little excess radiation, sometimes it lets go a little excess heat.

The atmosphere has natural "oscillation modes" that exhibit oscillations in time and waves in space, in pressure, density, and temperature, accompanied by small surpluses or deficits in the "heat balance." You're familiar with some of these oscillations and waves as hemispheric and quarter-sphere oscillation modes with names like El Niño/Southern Oscillation and North Atlantic Oscillation. (Think of the atmosphere as a spherical drum wrapped around the Earth, and you'll get the picture.) They aren't exactly periodic, like a clock. They're a more like a drunken clock that never repeats exactly the same way twice.

The nature and importance of these oscillations will take up a later posting. But next we'll see how the heat flows shape how temperature is distributed. The combination of split-up and secondary flows and variable "heat-capturing" efficiencies is what determines specific temperatures values.
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* Not all atmospheric heating comes from below; the 19% represents direct energy input from the Sun into clouds. The upper atmosphere is heated mainly by direct absorption of solar radiation, although it's a small fraction of the total solar energy flow.

** Sometimes we get dramatic reminders of this, as when hailstones fall from very high, very cold altitudes and hit the ground, unmelted - on a hot summer day.

Another thought on the drug war

It's the old joke about psychologists and light bulbs - but it's really not a joke. It applies to drug abusers as much as to alcoholics. And we do no one any favors by simply banning the substances, rather than the consequences of abuse. The abuser is the real problem - but they have to be convinced or, more likely, convince themselves, before any change can happen.

Classical music radio R.I.P.

Is there any industry in America more confused than broadcast radio? Here's what the Washington Post's Howard Kurtz has to say:

All these folks (including me) are paying for satellite [radio] because they're tired of cookie-cutter radio formats stuffed to the gills with commercials. They're also fed up with focus-grouped music stations that play the same 60 songs until you start hearing the chords in your sleep.

And local radio stations covering news? There are a few across the country. For the rest, forget about it.

Really, can you think of an industry (okay, maybe American automakers) that has frittered away such huge advantages and sent its customers scrambling for alternatives?

Guess not. One of the really distressing aspects of this overall decline of broadcast radio is the decline of classical music radio. One station after another of this venerable industry is being sold to create yet another unneeded sports or top-40 station. Each of these stations will be chasing the same stagnating pool of advertising revenue and drive away more listeners.

The most recent casualty is Washington's WGMS, once a flagship of classical radio. It switched for good from classical broadcasting in January. (Fortunately, public radio WETA took over WGMS' call letters and repeater and switched back to classical from its former news-talk format. And Baltimore still has the great WCJB.)

WGMS follows hard on another recent causalty (wounded, not dead - yet), Boston's WCRB, which recently switched to a different frequency, lower power, and programming even more dumbed down than the recent trend in classical radio, which was bad enough. When the big classical radio audience changes happened in the 70s and 80s, the trend was to eliminate opera and obscure works. Short works were in demand for drivers in the morning and afternoon rush hours. But in the 90s, the trend got much worse - longer, more difficult, or lesser-known works of all types were eliminated at all hours, and the playlist reduced - like the pop playlists - to the same 40 or 50 works, repeated incessantly, along with ever growing time devoted to ads. Whole works are now being cannibalized for movements - anything that can be played in under 10 minutes.

The obvious explanation, changes in audience, is off the mark. The same trend is visible at non-commercial public radio stations, which have been dropping their jazz and classical programming in favor of more and more news and talk, even when listeners don't want it. The problem is the people running the industry: in the commercial sector, they will not budge from the totally safe formula; in the public sector, they won't give up the pretense of 'round-the-clock "serious" journalism. You can't fill 24 hours in the day with "serious" journalism - there isn't enough to go around. But you can fill it up with music - not just the standard composers and works, but lots of beautiful lesser knowns as well.

The result will be what Kurtz predicts: listeners will jump ship to satellite or Internet broadcasts as soon as they can. There's no evidence that listeners want more news, more ads, or the same playlists repeated ad infinitum. FM was once a haven for better-quality broadcasting, but the same forces that destroyed AM are now destroying FM too.

Ending the drug war

An interesting post yesterday on the failed Drug War over at Arianna Huffington's blog was enough to provoke some comment in the blogosphere.

Is there any current policy more dumb than the Drug War? If there is, I can't think of it. It's a major bipartisan disaster. The fact that's it bipartisan is, I suppose, the reason nothing is done to change it.

The Drug War has done far more damage to civil liberties in the last 35+ years than anything connected with terrorism or spying. The Supreme Court has even gone so far as to carve out large exceptions to the Bill of Rights to keep it going, eviscerating the Fourth and Fifth Amendments in particular. Pre-trial property seizures are now enough to keep some police departments in business without the need for taxes. And we all know what happens when government's revenues are disconnected from democratic control. Even worse are the no-knock raids that sometimes kill innocent people, often for no reason. No-knock raids are justified only if someone's life is in danger. Even giving the police the benefit of the doubt in ambiguous situations would end most of these raids.

And the policy has been, from the start, a complete failure. Drugs are not less available than they once were. Only in the world of politics is failure an incentive to redouble a failed policy. Huffington's post on the subject is motivated by another glaring Drug War injustice, the fact that black and Latino drug offenders are convicted and incarcerated at a much higher rate than white drug offenders. (This is after you take into account the fact that drug users are disproportionately black and Latino to start with - there's still an extreme imbalance in both the rate of conviction and the severity of the punishment.) It's not as if the policy was intended to be racist - most black and Latino politicians are, if anything, more in favor of the Drug War than are white politicians.* Unfortunately, that leaves politically less powerful "people of color" more vulnerable to out-of-control law enforcement. After all, educated middle and upper class people tend to complain more and more effectively when their rights are trampled on, and in politics, the squeakiest wheel always gets the most grease. The injustice of incarcerating a couple million non-violent drug offenders, in already overcrowded jails, is rarely remarked upon.

And I haven't even mentioned what the Drug War has done to American foreign policy. It makes relations with many Latin American countries more difficult than they need to be. But the worst thing it does is to create an artificial market for expensive, illegal substances whose inflated profits bolster and arm some of the world's worst criminal organizations, including the Taliban in Afghanistan and Colombia's FARC guerilla movement. It pulls farmers in poor countries away from growing food towards the much more lucrative growing of poppies, marijuana, etc.

What should be done? We must start with the recognition that there's nothing romantic about drug abuse, in spite of the psychedelic nonsense planted in some people's heads in the 60s. Like alcohol, psychoactive drugs can be used in a limited way for an occasional high - or they can destroy users' lives. But the Drug War is a larger, longer-running, and more expensive version of the failed Prohibition of the 1920s - and Americans then had enough sense to end that. Our society since has learned more positive ways of limiting alcohol consumption and discouraging its destructive misuse. It's not an accident that Alcoholics Anonymous, the world's most effective program for treating substance abuse and a model for many other similar programs, was started in 1934 - by private, voluntary initiative - immediately after Prohibition was repealed.

At a minimum, the "Drug War" itself should be stopped, even if possession and use remain felonies. That would mean an end to the special status that fighting drug offenses has in American justice and law. (The federal Bureau of Alcohol, Tobacco, and Firearms, a Prohibition-era relic, should be folded back into the Justice Department.) A much better and more comprehensive change would be to drop possession and use to misdemeanors, leaving selling as a felony. Ultimately, certain less harmful drugs could be decriminalized altogether. (Possession, use, and sale to minors would remain illegal.) If drug users on a high pose a danger to others, they should be treated as we now treat drunk drivers.

Imagine what that would be like. No more property seizures. No more no-knock raids. No more wondering when it might be possible to vacation again in Colombia. No more violent Third World thugs surfing on drug profits. It might even be omnipartisan - conservatives, libertarians, and lefties like Arianna overcoming the idiocy of brain-dead bipartisan "consensus."
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* I should mention an honorable exception to the rule among black politicians, Baltimore's former mayor Kurt Schmoke.

And a long, strange journey it was

I used to think that it would have been better for the weekly Torah portions in the early part of Exodus to fall at the same time as Passover, but now I'm glad they don't. Let me explain.

It's one thing to read the original of the story, get through the drama of "Let My People Go" and the crossing of the sea. It's another to read the Haggadah of Pesach, which is the same story filtered through centuries of commentary and analysis, not to mention our own personal experiences. Having both at the same time would be too much.

The interesting thing about Pesach is how it marks the end of two months of orchestrated crescendo, starting with the first hints of spring at Tu b'Shevat (which features its own miniature seder), then the not-quite-supernatural salvation of the Purim story, and then finally Pesach itself, with divine presence manifest and obvious.

Happy Passover

A chag Pesach kasher v'sameach from Kavanna!