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[wierd]

well, if we just *ignore* the nighttime plateau issue, and just look at daytime temperature variations alone as a normal distribution, then we can abuse some rules of statistics to smooth the curve out.

That's really bullshitty though.

It would allow us to get an estimated period for daytime exposure though, which could then derive as a rotational velocity, and thus derive distance. That would give us half the theoretical circumference of the longitudinal circle where the temperature measurement was taken, and thus be useful. (But again, we would be discarding the nighttime data wholesale.)

Unfortunately, my brain is very unhappy with where that can lead... the "best" topology will probably be non-euclidian, on a complex coordinate system. The second best probably a halo type ringworld with very fast rotation. (The first one is only explicable mathematically.)

The first option explains the difference in light levels at different "longitudes" using an imaginary spacial axis (not a time axis! An actual space axis.) The light travels more distance through the imaginary axis at higher (or lower) latitudes, but te world this otherwise a cylendar when viewed in 3 dimensional space. This is why the map doesn't get distorted, while still being colder the greater the distance from the equator.

The second one helps explain the plateau in night time temperature, but has issues with curvature based distortion of the map. Basically, the surface at night is always seeing the the sunlit side of the torus, because the torus is inclined to the plane of the ecliptic by some angle. (That means it is getting lots of reflected light, even at night!) This explains why the energy at the equator is what it is (angled to ecliptic), and It may also explain the seasonal variation as well. (Rate of precession is exactly matched to yearly orbit, so that total angle of pointing is always on the same vector.) However, this makes a twice per year period where the torus eclipses both surfaces, making it totally nighttime, which does not happen in game. A possible solution comes from making the "moon" into a gas giant, which the ring world is orbiting in a very peculiar way. (But it makes the southern hemisphere always colder than the northern one.)

In this case, we have the same inclined torus, orbiting transversly to the to the plane of the ecliptic, around a large gas giant with its rotational pole aimed at the star (like uranus), in a slightly tilted orbit in relation to the planet's plane of rotation.

This means that the surface of the ring world will see variations in the amount of lit surface of the gas giant it is orbiting, as it moves "above" and "below" the plane of the planet's rotation. It does not go into the planet's shadow. This movement also alters the ringworld's insolation value, because it moves farther away from the sun as it transits the planet's rotational plane, then coser again as it transits the second time. This would explain the perfect synchronicity of the "planet's" year with the "lunar" cycle. The ringworld is orbiting the moon, not the other way around, and that orbital cycle is what creates the illusion of the "year".

The actual solar transit period of the gas giant's year may be considerably longer.

Illustrations may help with this. I'll see what I can come up with.

[itg]

I'd love to see what you come up with as far as ringworlds and non-euclidean planets, but I'd also love a more detailed explanation of why you think it's necessary to go there. I mean, even if we agree that there's something wrong with the DF temperature dynamics, and I'm not sure I do (the desert temperature graph, at least, is qualitatively similar to a typical real-world one), wouldn't weather patterns be the natural place to go next? And why demand that DF temperatures behave a certain way, when Earth temperatures don't even behave that way?

[wierd]

In order to derive angle of incident at a given time interval, we need a uniform curve over the daylight hours. (Morning and afternoon fall off cleanly on either side of noon.) Otherwise, we need a complex orientation to the sun to account for the sharp fall off. I can get that (I think) with a ring world cocked at a funny angle. That would let the evening side be slightly more sunward, and fall off more sharply than the morning side, and would allow the midday energy curve to stay plateau shaped regardless of latitude.

It also explains the incline snaake(?) Derived for previous insolation estimates, without making the planet hugely bigger, and making the equator hotter than death valley on its coolest days.

It also forces the lunar cycle to match the yearly cycle automagically, and keeps map distortion at the polar regions at a minimum.

It isn't just the temperature data that is involved.

OK, unvalidated mental picture time.



Sorry if this is blurry. Photobucket hates bmp files and makes them jpegs, and does bad things. I usually use png, but was in a hurry.

Here we see the basic layout of the system. The sun's axis is straight up and down. The gas giant "moon" orbits the sun counter clockwise. Its axis is always pointed directly at the sun. The ringworld orbits the "moon" prograde. The ringworld's orbital path is inclined from the planet's plane of rotation. (Not easily seen. The two look the same direction at this angle of view. Sorry.) The ringword itself has an axial tilt against its orbital plane, so that its pointing vector always stays at a fixed angle to the star. It rotates counterclockwise on this tilted axis. This axis is tilted in 2 angles of direction, so that the evening side of the ring is more sunward than the morning side, which causes the "plateau" on daytime temperatures ring-wide, and makes evening insolation fall more sharply than daytime. The difference between morning and evening curves should be complimentary of the ideal sinusoid curve. (Unchecked.) At night, the daylight side of the ring will yawn brilliantly overhead, and will reflect considerable nighttime light on the surface, reducing the rate of cooling all night long. The inclined orbital path of the ring in regard to the gas giant makes it take a kind of "spirograph" orbit. The completion of each node of the spirograph is a lunar month, and the completion of the whole transit is the year. The solar year of the gas giant is moot.

Here we see the mental sketch on the side, better showing cocked angles.


Until I (or somebody else) does the math, this is conjectual, and should be viewed as exactly that.

[itg]

Pictures look great. I'll have to think about this later. In the meantime, here's temperature data from a second desert, a day's rampage north of the first one:

Spoiler (click to show/hide)

1   29
2   40
3   51
4   55
5   60
6   64
7   69
8   70
9   70
10   70
11   70
12   70
13   69
14   57
15   47
16   36
17   27
18   27
19   27
20   27
21   27
22   27
23   27
24   27

This is data for the 20th of Malachite. As there was no interference with the measurements, for a change, I only had to do one day's worth. No surprises here, but, in addition to the plateaus, this is the third location out of three with a "hump" in the curve at hour three. At this point, I'm comfortable saying that hump is clearly a feature of DF's temperature model, not an artifact of my measurements.

[Snaake]

...
So, from the data we know that:

• There are set "target" maximum (daytime) and minimum (nighttime) temperatures.
• Heating is either sinusoidal or logarithmic, but cooling is linear.
• Daylight hours are a bit whack; if the hot edge of the map gets 16 hours of daylight, even if it's only at the summer solstice, that would mean the equator is actually still quite a ways off, and probably quite !!FUN!! (what's called a scorching desert in DF would probably feel refreshing after a walk at the equator).

I realized some erroneous assumptions/conclusions in my previous post (the short list of conclusions is above, but there's some other stuff too). First of all, cooling in itself isn't necessarily linear, but the effect of lower insolation late in the day (as the sun is setting) and the cooling has a total effect that looks linear. Or my new guess is that maybe the sun sets at around 13 hours of daylight (the cooling isn't completely linear before that, showing that there could still be some small heating), after which cooling is linear as speculated earlier. So the daylight hours are also a bit shorter at the South map edge, but still about an hour longer than expected for the equator, which should be a few minutes over 12h year-round (google e.g. "length of day Quito" or Singapore or something, check January&June). Also found this nice visualizer. 13 hours at summer solstice corresponds to about 17 degrees north, which would mean that the equator would still be somewhat habitable: at worst, only about as bad as the existing scorching climates.

As a side note, It's kinda annoying that the plateaus are so big, with enough accuracy (1 degree F or U should be enough, I think), there should be a curve visible over the whole day, or at most a couple of hours of even temperatures. In real life, you need averages e.g. off the same day every year for several years to get rid of weather effects, of course. Also, lack of a clear peak/trough means it's harder to pinpoint what kind of delay specific heat capacities introduce to the system.

Readings from a desert/rocky badland vs. ocean on the same latitude would be interesting, since it might help isolate the effects of latitude vs. surface material. The desert reading definitely suggests my "target temperature" claim from the quote above, since barring statistical flukes due to weather, you wouldn't get plateaus that flar in real life, pretty much ever, at least not at tropical latitudes. So yea, the temperature model is "broken", or to put it another way, pretty simple, and doesn't fully take into account how high temperatures can reach during the day and so forth. My guess is that the max. temperature plateau might actually a safety feature for gameplay, to prevent dwarves from melting in scorching climates. The low temperature plateau is probably a "minimum ambient temperature" defined by latitude and/or biome, that cooling occurs to.

Regarding the temperature plots from Phoenix, yes, temperature does flatten out a bit especially on warm days, but I'm not totally convinced by the examples yet, either. Like I've said, one, or a few, days do have slight weather fluctuations even in a desert with little to no "weather" as usually defined in temperate zones (rain, clouds, etc.). Also, the y-scale is really flat in those plots, leading to an illusion that the temperature is more even that it is. Possibly.

Oh, and we have different energy units because the calorie was probably invented first; it's pretty easy to define experimentally, you just need a heat source, a thermometer, and a scale (to measure how much water there is), and a closed water container to prevent evaporation. However, it's not a neat, SI, base-10 unit, unlike the Joule. Why are there (in the imperial system, of which "you Americans" are the last big die-hard users) so many arbitrary units of distance/time? At least the calorie is somewhat scientifically defined.


...and finally, regarding the 2nd sand desert plot, yea, I'd say the "hump" is a feature of the heating model. Either the insolation function only approximates a sine curve with linear segments, or the temperature curve is formed directly, and the slope of temperature increase is just set to drop by some % 3 hours after sunrise.