The Fallacy of Trapped Heat

I was pondering the problem of lighting a sphere and figuring out how much energy arrives where. This led to two interesting web pages (that I’m trying to find again). One was a scholarly look at it from a “climate science” perspective, that proceeded to list a load of critical things that would be simplified out of the problem. The other was an animation rendering paper that found an ‘almost right’ and good enough method for calculating lighting that gave much faster rendering times. The Animation Folks took on the problem in a much more complicated way (even though it was a dramatic simplification of what is used now in rendering). The “net net” for me was that clearly since ‘it has to look right’, the animation folks did a LOT more work on the problem. This implies that the “climate science” folks are leaving out a load of reality. Reality that matters, or it would ‘look right’, and the animation folks would not need to do such complicated things. But the details on that will need to wait for another day, when I have the URLs in hand.

What it did do is remind me of just how complicated the world is and how much the details matter. Was there a way to garner some useful information from that perspective?

Several times I’ve ranted that temperature is just the wrong thing to use to measure heat. Basic physics. Temperature is not heat. Temperature can’t even tell you about heat. It is an intrinsic property of one object (or one part of an object). Heat is an extrinsic property. You need mass, and specific heat of the material, and any phase change information; then you can start to talk about heat. OK, that said, I’m going to be sloppy for a little while (in that “climate science” kind of way) and talk about energy flows in and out, temperatures, and yes, even reference heat; all while not being scrupulous in keeping them isolated from each other (like they ought to be).

So I was picturing a sphere being illuminated by a distant point light source, with a variety of reflections (moon, planets) and with constantly changing surface texture and reflectivity (clouds, ocean) and just what WAS the illumination of any one spot? The illumination of a wave crest on the tangent of the perimeter may be normal to the incident sunlight, while the trough of the wave is in shadow, or at such an angle that any sunlight is reflected off. The surface “roughness” varies, dramatically. As for “average illumination”, that’s a bit of a lark. What is the illumination at the South Pole? Would that be December or June? So we play with numbers to get an average over a year (or years) and pretend that is what is happening. But it isn’t.

Every day nature runs an experiment in illumination. It starts out ‘near zero’ (but not AT zero, as there are stars and moon to think about, and those pesky clouds). Then slowly rises to ‘full sun’, and heads back to ‘near zero’. In other postings I’ve admired the point that we “ignore the day at our peril”. Similarly there are seasons. Over a one year period, we move from winter to spring, then summer and fall. Then back to winter. Simple, no? But what does that say about “trapped heat”? It says that on a seasonal level, heat leaves. Massive quantities. We go from 110 F in the shade (“and there ain’t no shade”, as I’m fond of saying of summer in my old home town…) to 20 F and a load of frozen water. Where is all that “trapped heat”? Hmmmm? Can we put a “size” on the heat flow? A “rate”? I think so, even if it is a bad, or poor, one.

The basic thesis of “climate science” rests on the notion that “heat” will “build up” in the system. That it will be trapped over a duration of decades and raise the temperature. Yet we know that heat does not “build up”. It leaves. Every winter demonstrates that on a longer term scale. Where is summer heat when winter snows arrive? Gone.

It didn’t go furtively into the oceans. It didn’t run off to Brazil with the maid. It didn’t crawl down into the earth to make volcanoes. The Elvis of heat has left the planet.

At any one time, there is ONE spot on our planetary sphere that takes a path directly normal to the solar disk. Over the course of a day, that traces a single circle around the globe. Everywhere else is a bit ’tilted’ relative to that line. Getting ever more oblique to the sun, and not as hot. The further you get from that equatorial line, the colder you get. The heat is not “building up”, it is moving. Maximum on that line, lowest at the poles, and moving massive quantities of water and air between the two, trying desperately to equalize the temperatures, and failing. Because the heat leaves. Every single day, and every single season.

Now that line wanders back and forth with the tilt of the earth on a seasonal basis (causing the seasons). It stops at the two ‘tropics’. The Tropic of Cancer and the Tropic of Capricorn. (Echos of when we referenced the starts and constellations to maintain our orientation in life…) As that line moves the heat moves with it. We do not have “trapped heat” at the Tropic of Capricorn keeping it nice and warm all winter. Summer heat rapidly leaves. Winter comes. Much further from the equator we have places that never do get “normal” to the sun. It is always a bit low on the horizon, never directly overhead. (The ‘tropics’ mark the limits of where the sun can be overhead, even if only briefly on one summer day). Those places are never quite as warm as the equator. Try as it might, the earth just can’t move the heat there sufficiently to warm those poles before the Elvis of heat has Left The Planet.

Now return again to that sphere spinning and nodding in front of a light source. It gets 100% of illumination on one dot, that rotates a bit over and gets a bit less while another dot rotates into position to get a bit more. One polar end gets some decent, though not direct, illumination, and another gets darkness in shadow (yet with cloud reflections and such to complicate things). What temperatures do we get? From about 50 C down to about -50 C. A 100 C range. From tropical / desert to polar / arctic. We can size the range of illumination (moderated by huge heat flows in water and air) at about a value that gives 100 C of “range” from “full” to “zero”. Now take those places that have more consistent daily illumination. They have daily temperature swings, too. We could, in theory, take those daily temps, compare them to 100 C, and figure an ‘efficiency’ of heat storage over a daily cycle or over a seasonal cycle. (It isn’t really an efficiency, but I’m not sure what other term would give the idea well. It’s more a ‘figure of merit’ but that’s a bit vague as a term.)

So right now I’m in Florida in the early Summer. The sun is nearly overhead at high noon. Daily temperatures cycle between about 74 F at night and 94 F in the day. Yes, both ends ‘wander’ a bit with the passing storms, or sunnier days; but it tends to hang about there. In south Texas, at a similar latitude, it can have a much wider range. They have less water to store heat as non-temperature things like enthalpy (heat of vaporization / condensation).

Now those 20 F degrees are about 10 C degrees (really 11.1111 but the error bands on the estimates of the range are greater than 1 C so 10 C is ‘close enough’). That’s 1/10 of the 100 C range from “zero to full”. That means that in one night, Florida, great as it is at storing heat in all that ocean water around it, dumps 1/10 of a “full load of heat”. (It dumps more during the day in those thunderstorms, that’s why it’s not 50 C and tends to drop back to ’80 something F’ after an afternoon storm) It doesn’t dump it to the poles (we don’t have winds running 6000 miles in 12 hours, or 500 MPH toward the poles…), it dumps it off planet. (At cloud tops in all those nice rising thermals freezing tons of water to plummet to earth, melting on the way, and making nice afternoon downpours).

Over the course of a year, as the seasons change, the high and low move together with the seasons. At the low end, we start to get more range. Why? Because the hurricanes and thunderstorms that are the convective engines in a hot wet environment stop working. Their heat engine turned off, they remove less heat. So a winter day max can rise further from a winter night low before starting up that heat engine that puts a lid on temperatures at about ‘mid 90s F’ here.

Similarly, once water freezes, it can not give up heat of fusion to moderate low swings any further. So winters in places like Calgary Canada, can get quite cold. Water moderates the downside to a point, then stops, where summer storms can just get bigger, more frequent, longer lasting, and move ever more heat. The heat there comes with the summer sun, and is gone when the sun drops low on the horizon.

In my old home town, winters got down to about 20 F ( -7 C). So from 43 C in summer to -7 C in winter. 50 C of range. Now the Topic of Cancer is at about 23 degrees N, while my home town was closer to 38 N. That means we never quite got directly overhead sun, even in the hottest part of summer. A good 15 degrees off ‘head on’ normal. Yet we got to within a few degrees C of some of the hottest spots on the planet. And in winter dumped all that heat to be 1/2 way to zero sunshine. Even though the sun was well above the horizon and the ocean only about 100 miles away. Where is all that “stored heat” when you need it?

Daily temperatures could be as low as 20 F, or sometimes only 50 F, at the winter cold end. Sometimes winter days were about 30 F peak, sometimes 70 F. It all depended on how much sun we got and if a polar cold air mass landed on our heads. The mobile polar air could knock us down about 10 F. The rest was solar and heat loss. Warmer air could put us up 10 F, but if the next day was poor in sun, we got cold. Overall, the warmth of the day was strongly driven by daily solar heating, moderately by movement of air masses. Water uniformly made things colder. (When a storm would come, it was always cold rain, or hail, and occasional snow; never a warm tropical rain). Here in Florida, we have a warm tropical rain; but even that knocks the temperature down several degrees in minutes.

So again, where is all the heat “trapped”?

Simply put: It isn’t.

There is seasonal solar warming of tropical oceans that drives the ocean circulation and dumps that heat into the polar oceans; where it leaves the planet during long cold polar nights on a seasonal basis. There is daily solar warming of tropical and temperate regions, that drives daily thunderstorms (or cyclones where there is enough energy input) that moves heat to the stratosphere (and off the planet). On daily cycles, we can see a large part of the heat leaving in the water cycle in tropical and temperate regions. On a seasonal cycle, we can see the remainder leaving from the polar regions (delivered by ocean currents, while keeping things at least a little livable near them as it flows by). We can size those daily heat flows as being about 1/10 of a zero to full peak solar heating in any one day on land. (Though oceans can hold some heat a bit longer as it runs for the poles).

The heat is not trapped. It is not subject to ‘runaway feedback’. It leaves, rapidly, and the daily and seasonal variations that we see track the changes in solar input very rapidly, indicating just how fast that heat leaves. The peak summer heat comes about 1 month after the peak summer sun. There’s a bit of heat stored in warming soils and waters. About 30 days worth. (That’s the lag time of the storage). By dead of winter, it’s all gone again. Raise summer heat by 10%, you bought yourself about one day of cooling needed to dump that excess. At most you can slow the worst cold of winter by a couple of days.

For a formal treatment, this ought to be put into a load of formulas with heat storage in water and soils showing a one month lag on seasonal sunshine changes, and with overnight moderation of temperatures to match the daily ranges at each place sizing the local water cycle. Showing speed up and slow down of ocean currents with lunar tidal forces and thermal driving. For a ‘getting it’ moment, simply realizing those heat flows is all it takes. Trying to imply some “global warming” out of an average of an ever changing population thermometers is a fools errand. It ignores the herd of elephants in the room. Enthalpy. The water cycle. Ocean currents. The ever changing illumination of our sphere as it rotates and nods. Clouds and thunderstorms. All those things that move and dump the heat, leaving temperature as a poor proxy in a chaos of water and precipitation. You simply can not ignore the weather when talking about a 30 year average of weather.

So to the question of “Where is the trapped heat?”, I answer “It isn’t. Elvis has left the planet”.

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