An Example of Fractal Temperatures

Steam On A Fence at 40 F air 60 F surface

Steam On A Fence at 40 F air 60 F surface

Sometimes nature does some truly beautiful things. One of them is the sight of steam rising from a surface on a Very Cold Day.

Yesterday, the air temperature was about 40 F on the back patio in the shade. ( I have a picture of that thermometer, but don’t feel the need to upload it, as for 3 MB of limited storage, it’s just not that impressive a picture. I just took it for photodocumentation purposes. But be comforted that I do in fact have that photo complete with time stamp.)

When I went to the front porch at about 11:30 am to let the cat in ( it was cold and wet out, and Mr. Cat wanted warmth, love, and food; in roughly reverse order…) I noticed one of my favorite phenomena. The “hot steam on a cold day” as sunshine warms a surface and evaporates the wet, but just millimeters above the surface it condenses again into steam.

I ran for the camera and the thermometer…

Here was a great chance to measure and document just how much variation there can be in surfaces over a very short period of time and space. The back and the front are about 50 feet apart.

So I put my ‘photo chemical’ thermometer on the fence. It’s a fairly fast reacting and very accurate thermometer (or your pictures come out wrong…) The sun had just come out after a fairly heavy cold rain. Everything HAD been roughly the same temperature 1/2 hour before… The question was: How fast and how far can surfaces warm in the sun on a cold wet day?

The answer:

Temperature on The Fence Top

Temperature on The Fence Top

A bit under 20 F hotter.

So this is a very simple example of the highly variable nature of temperatures. To some extent, it illustrates the dependency of air temperatures over a surface on the very nature of that surface. As the surface of the planet is fractal in topology, that implies that temperatures over the surface of the planet are also fractal in nature.

When we measure “global average temperature” we are simply measuring the error band in our instruments. The size of a measurement of a fractal surface is directly controlled by the size of the ‘ruler’ used to measure it. As we are constantly changing the number and location of thermometers used to measure “global temperature” we will get constantly varying results, even if the state were constant.

What makes “1 meter over the surface” more or less ‘right’ than 2 meters? Or 1/2 meter? What makes ‘over grass’ more or less right than “near the runway”? As we keep changing those things, we simply get closer to that 40 F or that 60 F from the same small place on the very same day and time…

FWIW, note also that all that steam rising is taking one heck of a lot of heat with it into the air. The water evaporates at a constant temperature, so we have massive heat gain with no temperature change. Then that heat is given back into the air as the condensation happens. Here we see it happening in millimeters. With clouds and oceans we see it happening in miles. That picture also illustrates the stupidity of using temperature as a proxy for ‘heat flow’. The actual heat flows are much much higher than that temperature differential suggests. ( about 1/2 kW / m^2 on the fence top, about zero on the patio… yet a meter up in the air over the fence, it’s all ‘disappeared’… gone into vapor instead of temperatures…)

About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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14 Responses to An Example of Fractal Temperatures

  1. Tom Bakewell says:

    Nice post. Concise language covering what shouldn’t be that difficult to understand, at least for those who care to investigate. Thank you sir.

    PS whatever did catcreature get named?

  2. E.M.Smith says:

    “Magic”. As a kitten he could, and would, escape from any and all possible enclosures, including the whole house. So we named him ‘Magic’ as he surely was. Finally discovered that he got out through a 1 inch or two ‘gap’ between a window screen and frame if pushed on just right…

  3. gnomish says:

    once vaporised, that moisture is very buoyant and rises away very fast – something like 1 km in 10 minutes.

    and no BB spectrum show it.

  4. Jason Calley says:

    Just as you will find surprisingly warm surface temperatures for a given air temperature, you can find surprisingly low temps as well. In a former incarnation I used to do a lot of all night amateur astronomy gigs. Many late nights, just before sunrise, I would find frost on my car, even though the air temperature had never dropped to freezing. When the sky is clear and dark, an exposed surface can radiate enough heat into the night sky to create frost. The air might be 2 or 3 degrees C and STILL the blasted frost forms. I met several people — moderately bright — who swore that I must be wrong about the air temps, must not understand science or must be lying. Nope.

    By the way, in the high deserts of Chile, the locals used to create ice by this process. Place shallow pans of water in areas that have a clear exposure to the night sky, and you will find ice in the morning.

  5. Malaga View says:

    Great post that has got my grey cells moving this morning… although I suspect it is my morning blast of nicotine and caffeine that really gets them started… it is this buzz that then gets me searching the internet for some brain food… so thank you for the mental munchies.

    Now I am trying to resist ranting about the concept of a global average temperature… the topic drives me nutz… well that is not totally correct… it is the people that promote this concept that really drive me nutz… this is because I just cannot understand how supposedly intelligent and educated people can be so dim… so either they have an agenda and / or it is another example of Fractal Intelligence.

    However, the main event currently bumping around in my fractal brain is how Greenhouse Gases move around in the atmosphere… so your beautiful steam rising photograph really grabbed my attention. Remembering back to my school days I remember I was taught Hot Air Rises and this was wonderfully demonstrated by the pioneers of hot air balloons… and more recently by Al Gore and the AGW religion… but I digress.

    So the sun heats the water on your fence… the warmed water evaporates into the cooler air above your fence… and the rising water vapour then condenses as it is cooled down in the cooler air. Now I am OK with this so far… the bit that gets me is this: How does this water vapour manage to rise up thousands of feet to form clouds?

    In your photograph it looks like the water vapour is giving up its heat very quickly… so the 20 degrees F heat differential gives the water on your fence enough energy to blast off into the atmosphere… but that energy is quickly dissipated… so what keeps the water vapour rising? Perhaps the sun begins to heat a wider area… say the whole backyard… even the whole street and neighbourhood… and thus this bigger body of air begins to rise and takes the water vapour along for the ride.

    But now we hit the lapse rate… as hot air rises it cools down… and an average value I found for this is about 2 degrees C (3.5 degrees F) per 1000 feet… so the water vapour will probably rise about 6,000 feet before it has lost all of that 20 degree F heating it got while sitting on the fence… and this seems to fit well with the definition of Low Clouds according to Wikipedia… so I am a happy bunny so far.

    So my next question is: Why do clouds just sit there in the sky? Why doesn’t this cooled water vapour immediately fall back towards the earth? Surely if hot air is rising then cool air should be falling? So this is where I think it might be getting interesting… perhaps the water vapour in the clouds is now acting like a Greenhouse Gas… capturing some extra heat from the sun… capturing enough extra heat to stop it falling back to earth like the other cooled air… and perhaps the water vapour captures a little extra heat when it is rising up… so perhaps water vapour accelerates away from the other rising warm air,

    Still with me? Good. Now I get to the thing that really puzzles me:

    If CO2 is a Greenhouse Gas then why doesn’t it behave like water vapour?

    More specifically:

    Why don’t we have clouds of (invisible) CO2 in the sky?
    Or is it that we just can’t see them?

    Why doesn’t all that heavy CO2 in the air fall to the ground when the air cools at night?
    Why don’t I wake with clouds of CO2 swirling round my ankles?

  6. gnomish says:

    phase change, MalagaView, and enthalpy. on our planet, co2 doesn’t have it; only water does.
    plus, water gas is the lightest gas and requires no convection to rise in our atmosphere
    that makes a continual flux any time energy is put into the surface and every other gas, kinetically sharing the same temperature, must go along for the ride to that infinite heat sink in the sky

  7. Malaga View says:

    Thank you gnomish… that gives me plenty to chew on… I shall try to inwardly digest this information into my finite memory sink.

  8. DirkH says:

    As long as the Niquist (or Shannon) theorem is violated, computing an average temperature (or anomaly) is simply meaningless. So GISS computes a meaningless number in more or less the same way year after year, and the meaningless number happens to go up slightly. Well, it’s still meaningless; it’s not well-defined; the number doesn’t tell us anything.

  9. DirkH says:

    Malaga View
    “So my next question is: Why do clouds just sit there in the sky? Why doesn’t this cooled water vapour immediately fall back towards the earth? Surely if hot air is rising then cool air should be falling? ”

    It is slowly being recognized that water droplets can acquire an electric charge. This should also tell you that much is still unknown, see also Svensmark. It is not only so that GCM’s can’t model half correct cloud formation by now; no, we actually do not have the entire knowledge about the physics involved – so we basically don’t know what to model.

  10. Malaga View says:

    Thanks DirkH… that gives me a good cop-out from going further into the physics… especially as I was beginning to feel I had entered if you convince them then confuse them territory… so I will sit tight and wait for a KISS – Keep It Simple Solution.

  11. GregO says:


    Did you take the “Steam on a Fence” photo at the head of this post? That’s a great shot!

    Yes, I wonder about the warmist crowd worrying about half a degree a decade level of so-called global warming. Considering the multi-physics going on within such a tiny range of delta-t I’m sorry but so-called global warming is nothing but noise in the data.

  12. @E.M.Smith:
    Sometimes nature does some truly beautiful things. One of them is the sight of steam rising from a surface on a Very Cold Day.
    Really!. We, “deniers”, “skeptics”, the “anathematized ones” are rediscovering the wonders of nature, the eternal laws that govern it, the “Canon” behind it, the real “Physis”. It doesn’t matter all lies and cheats promoted by the ones whose only purpose is keeping us “distracted”, “amused” or if that it is not enough, totally occupied in trying to survive, while they do their best they can do:” To pour the empty into the void” and make profits out of it,(Really by “pumping it out” from our pockets.
    What will change this, our “blissful existence” will be, precisely, this awakening, rediscovering these simple and marvelous truths:

  13. John F. Hultquist says:

    This explains why planting trees and putting in fence posts (both of which I do) at greater than mid-latitudes causes warming.

    About 10 years ago planting trees was the big thing – going to save the planet by cooling things down. “Not so fast” the researchers said, and we haven’t heard much of massive tree planting projects since.

  14. E.M.Smith says:

    @Jason Calley: I have to deal with that each winter as my car is parked outside where the windshield has a clear view of the (clear) night sky. It gets frost (and sometimes the top of the car) even when no other surface gets any and often when the night temp does not drop below freezing.

    It’s a ‘well demonstrated’ effect, even if some folks don’t thing so…

    @Malaga View: “Mental Munchies” I like that! … Glad I can help. Yeah, nicotine has ‘interesting effects’. If it wasn’t so addictive I’d be a regular user ;-)

    The “fence example” is but one form. Sometimes the water vapor forms over the topics, rises to great heights, moves to the poles, THEN condenses to make clouds. It’s a continuum with some condensing in centimeters an others condensing in kilometers. Water vapor is mol wt 18 while air is about 28 (N) to 32 (O) so water vapor of it’s own will rise rapidly. Until it condenses… even without the temperature ‘lift’…

    It’s a very dynamic process. Some sunshine is captured by clouds ( seen from below, a ‘dark cloud’ has captured about 1 kW / m^2 of sunshine in it) keeping them ‘warm’ and ‘rising’ only to condense further up. Some drop tons of snow, hail, and rain on us. Gigantic energy flows compared to CO2 and IR.

    Gases are mutually miscible. They ‘dissolve’ in each other. If you have enough concentration you can get temporary ‘puddling’, much like too much sugar ends up at the bottom of the coffee cup, but with a bit of stirring it blends in and disperses. Since CO2 is a solid (or liquid) only at temperatures lower than found on the planet, it’s this gas phase that matters, and it doesn’t ‘puddle’ well (modulo the bits fresh from volcanic sources at the ground surface).

    So water can condense and fall, but CO2, not so much.

    @Greg O: All photos in this posting are mine. I took the top photo, then ran in and got the thermometer. About 5 minutes all told, but the sun went behind a cloud and temperatures on the fence started to drop (note the lack of steam in the thermometer picture… so that 60 F or so is a LOW number as insolation was lower than in the steam picture…). I didn’t go into it, but think about the TIME dimension of temperature change here too. From steam to no steam in moments…

    And yes, you are correct about ‘noise in the data’. I’ve called it “Dancing in the Error Bands”…

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