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[itg]

It's only a cube map if you insist it be one. Imagine taking one of those identically-sized regions, shrink it 20%, and shift its position on the globe a bit. Now you've got a square region that doesn't tile. That may or may not be useful, but the point is that it gives you more options in terms of finding a projection which is compatible with gameplay. The Triangle-shaped region is not, because you can embark at two different sites near the north end of the map and they won't overlap.

There's also a possible compromise: a trapezoid-shaped region.

[wierd]

Agreed.. but the insolation values still need to jive with the topology you are laying it down on. There could be large "circular" zones at the top and bottom of the world that aren't displayed on the world map, but the curvature of the body has to allow that. (Again, "mooshed" sphere, or a torus.)

The ratio between the curvatures will define the topology.

[Snaake]

So, who's making the temperature-surveying adventurer? (I've never tried adventure mode, so... yea. Not me.)

[itg]

I'm willing to do it, but it will probably have to wait until the weekend. To really do it right, we should get data from different biomes, the same biome at different latitudes, and different worlds. Ideally I would do one world, and a few other people would make the same measurements on their own worlds.

For what its worth, you (or anyone who wants to join in the fun) could mod the game a bit to play as a bronze colossus, if you want to make surviving the adventure a (nearly) sure thing. I haven't tried this, but here's a post with plausible-looking instructions: http://www.bay12forums.com/smf/index.php?topic=131113.0

[wierd]

Ideally, the 2 best places to perform the measurements are at 60deg north, and 0 deg latitudes. Those are fixed points on the temp falloffs from legends mode, which very consistently fall the same number of world map tiles apart. This gives the length of curve #1.

Since we are wanting a ratio against curve #1, we should measure temp falloff over time at those two locations. This will give us the second length. (How many world tiles move right before 50% illumination occurs.) If the curve ratio is 1:1 at the equator, then the planet is a sphere. If the first one is longer, then the planet is an egg_shaped elipsoid. If the second one is longer, then it is a pancaked elipsoid. If the second one is WAAAAAAAAAAY bigger than the first one, then the planet is a torus.

Getting the "3rd curve" at the "60 degrees" line will further constrain the surface, because we can compare the lengths of time and total temp falloffs there too, and the distances between.

[itg]

I've started doing hour-by-hour temperature measurements in a new large world. Here's how I'm conducting the measurements.





This is Catig Strangleforded, the flying bronze colossus climatologist. I'll be sending him to interesting locations around the world to measure the temperature. The plan is to wait until dawn, read the temperature with dfhack's probe command, wait one hour, probe, etc.

To start, I chose to measure the temperature at the southern edge of the map, which is 100% ocean in this world. There were some frustrating technical issues. When crossing the ocean, there was a 5-10 second lag spike every 3-5 seconds, so in the end I had to tape down the DOWN key and walked away for a while. To use the wait command, I had to use tiletypes to make a solid platform to stand on. After waiting, the platform would disappear, and I would find myself half a screen from the map's edge. To move back to the edge, I had to endure another 10 seconds of lag each time, then I had to remake my waiting platform. Due to these inconveniences, I only tooks two days worth of readings. Here's a plot of the data:

Spoiler: Raw data (click to show/hide)

Day 1

1:    38
2:    47
3:    56
4:    60
5:    63
6:    67
7:    71
8:    72
9:    72
10:   72
11:   72
12:   72
13:   67
14:   58
15:   47
16:   38
17:   36
18:   36
19:   36
20:   36
21:   36
22:   36
23:   36
24:   36

Day 2

1:    39
2:    47
3:    56
4:    60
5:    63
6:    69
7:    71
8:    72
9:    72
10:   72
11:   72
12:   72
13:   66
14:   56
15:   47
16:   36
17:   36
18:   36
19:   36
20:   36
21:   36
22:   36
23:   36
24:   36

Hour 1 is dawn. Values on the graph are actually temperatures in Urists minus 10,000 U. For example, a temperature of 10,038 U will be displayed as 38.

As you can see, the data was pretty much the same on both days. The graph is surprisingly asymmetrical. The temperature rises relatively slowly and non-linearly in the morning, but falls quickly and linearly in the evening. The temperature plateaus in the afternoon and night, but the night-time plateau is almost twice as long. It will be interesting to see if this pattern hold in other regions, as well, and even more interesting to investigate why the temperature should behave this way.

[wierd]

If you are measuring water (and not the temp of your platform), then the specific heat of the water is likely the culprit. Toady *does* use specific heat values for materials in his calculations.

That this is water actually helps us to determine how much radiation is hitting the surface. (It takes approx 1 joule energy to raise 1 cc of water 1 degree celcius, if I recall that right. I will look up actual exchange rates later.) Very good that it is so consistent on its distribution. The plateau effect at night makes sense. The oean is deep, water mixes and sloshes around, and tempurature calcs work much like fluid flow calcs. While the upper surface of the water is getting heated, it mixes with deeper, cooler water. Water has a pretty steep specific heat, which means it holds heat quite well once warmed up. At nightfall, the water starts cooling on the surface, but all that deeper water it was mixing with during the day will still be quite warm. Mixing with that deeper water homogenizes the temperature. Planet-wide, the degree of insolation falls off the further from the equator you get, so polar latitudes favor cooling, which balances the equitorial region's favoritism toward heating. This is what drives deep ocean currents and weather patterns they cause.


However, we need to take the same measurements many places along the equator to fully silence any biases that might exist.

A better sinusoid curve should appear over a desert. Try generating a large region instead of a large island. It will have a chance of producing land at the equator.

[itg]

Actually, I was measuring the air temperature above the water, but the temperatures of the air, water, platform, and ocean floor were identical every time I measured all three. According to my measurements, altitude and water depth have no effect on temperature, either.

I suspect Toady uses a much simpler model for temperature calculations, where every tile which sees the sky obeys a single biome-wide climate model. That model may or may not be based on/inspired by real-life data. If specific heat is a factor at all, it probably effects the speed of temperature changes, and that difference may not be significant at the scale we're interested in. That is, it may be that air and water may differ in temperature for couple of in game minutes, but water "catches up" quickly, and the momentary discrepancy has no cumulative effect.

[Loud Whispers]

I must say, I am quite impressed and also disappointed that I never took my shambled lunar speculations quite so brilliantly as this.

However, there is one thing that puzzles me...

Impressive work and a very nice display. I never have the kind of patience required to pretty up displays - even very crummy displays tend to be an immense chore to link up. And improving a display by increasing resolution increases display element and link job count in a quadratic fashion.

Yeah, that display took up 97% of the time spent on this project, easily. I'm happy with the result, but it's not something I plan to do again anytime soon.

Since all of the Dwarven months are listed by material, couldn't you have substituted the massive blob of mechanisms for a hatch covering a row of materials, each representing a month?
I imagine invading the damned depths would have been less time consuming in order to reach precious usable slade than constructing this fine piece.

It starts on the 1st of "official" Granite, so new year's day is the same in both calendars. The months fall out of sync as the year goes on, to the point that official Obsidian is almost entirely Slade.

But it does accurately mark when a werebeast transforms at least?

[itg]

I must say, I am quite impressed and also disappointed that I never took my shambled lunar speculations quite so brilliantly as this.

However, there is one thing that puzzles me...

Impressive work and a very nice display. I never have the kind of patience required to pretty up displays - even very crummy displays tend to be an immense chore to link up. And improving a display by increasing resolution increases display element and link job count in a quadratic fashion.

Yeah, that display took up 97% of the time spent on this project, easily. I'm happy with the result, but it's not something I plan to do again anytime soon.

Since all of the Dwarven months are listed by material, couldn't you have substituted the massive blob of mechanisms for a hatch covering a row of materials, each representing a month?
I imagine invading the damned depths would have been less time consuming in order to reach precious usable slade than constructing this fine piece.

It would hardly be a megaproject if I did something so sensible and modest. That said, the reason I spent so much time on that display is mainly that by the time I realized, "Oh crap, this is going to take weeks," I was far enough in that I didn't want the work I had already done to go to waste.

Plus, Felsite doesn't exist in this version.

It starts on the 1st of "official" Granite, so new year's day is the same in both calendars. The months fall out of sync as the year goes on, to the point that official Obsidian is almost entirely Slade.

But it does accurately mark when a werebeast transforms at least?

It marks it accurately in the sense that it happens at exactly the same time each year, but the calendar actually updates about halfway through Granite 1, due the fact that the werebeast transforms back after the new year. Also, the calendar takes a few hundred ticks to process the signal. These minor shortcomings could be overcome by hooking the werebeast's plate to a signal inverter (so it activates the calendar when transforming into a werebeast) and a well-calibrated delay circuit.

[Snaake]

wierd: A Joule (J) is 1 kg * m² * s^-2. You're thinking of calories: 1 cal is about 4.2 J, 1 Cal or kcal about 4.2 kJ.

Also, I'm kinda skeptic about some of your claims about the plateaus making sense. Ocean water is pretty stratified, with only limited mixing between layers. For a very simple model, heat is transferred between layers and between the surface&atmosphere by heat transfer rate being relative to the temperature difference (for pure blackbody radiation/absorption, it would actually be the Stefan-Boltzmann law i.e. the difference between the 4th powers of the temperatures), so that cooling/heating is always fast at first and then slows down.

Well ok, the plateau makes sense, since the later slow cooling/heating could indeed look like a plateau, but it should be symmetric, not asymmetric as with the data. The plots look more like heating is just turned off at dusk, and the temperature drops linearly, as itg said. Also, whereever the measurements were made, it was (or should have been) summer at the time, since dusk occurred 16 hours from dawn. Also, on Earth, a daylight duration of 16 hours at summer solstice corresponds to roughly 48 degrees North/South. Which is a bit south of Paris, about the same as Munich, Vienna, Ulanbaatar, or a tad North of Seattle. Or about 150km South of New Zealand's South Island (pretty much open ocean all around the Earth, with the exception of southern Argentina/Chile).


Since insolation follows a sinusoidal curve over the day, I'd claim that average daily temperatures (so excluding weather effects, which DF doesn't have AFAIK) are also nearly sinusoidal, e.g. with this plot of water temperature over a year (the yearly plot is analogous to a daily one, which I had trouble finding just now).

Spoiler (click to show/hide)

What the large heat capacity or specific heat capacity (2 different things) does is delay the increases/decreases in water temperature compared to the insolation maxima/minima: solar heating is at it's smallest at the end of December, and at it's greatest at the end of June, and yet in the above "warm" coastal area water temperature plot, the sea water reaches it's temperature minimum in late January/early February, and it's maximum some time in August. The greater the specific heat capacity of the material, the bigger the delay. And if we include mixing/conduction of heat deeper into the material, the heat capacity and thus the delay grow. A sand desert (which also transmit heat downwards into the earth really badly, IIRC) would react quickly to changes in solar heating, both over the day and over the year, whereas oceans are pretty much the slowest thing to do so found on earth (possibly beaten at times by moist forests, both tropical and temperate).

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).

[wierd]

Awesome, thanks.  I couldnt remember what energy unit it was. (Why DO we have so many energy units anyway?)

The estimated insolation values for daily heating periods is definitely of interest. Looks like some very interesting geological phenomena would occur at the equator under such temperatures, when mixed with a water rich atmosphere.

The planet would be considerably larger than earlier calculations, and would be much closer to its star. That means perturbation of the moon's orbit would be greater as well.

The DF planet is looking considerably less habitable.

[itg]

Since sand deserts came up in the discussion, I decided do the next set of measurements in the nearest desert region. I found a nice one not far from the southern tip of the nearest land mass, probably about 10% of the way to the north pole. Later, I'll try to put together a map with the measurement locations marked on it. I did three days worth of measurements this time. It appears the temperature curve ought to be identical from day to day. The small day-to-day differences were caused by bandit attacks, which threw off the timing of subsequent measurements.

Spoiler: Raw data (click to show/hide)

Code: [Select]

16th Ma 17th Ma 18th Ma Avg
1 30 30 30 30
2 40 40 40 40
3 51 51 51 51
4 55 55 55 55
5 59 59 59 59
6 63 63 63 63
7 68 68 68 68
8 69 69 69 69
9 69 69 69 69
10 69 69 69 69
11 69 69 69 69
12 69 69 69 69
13 69 68 69 68.6666666667
14 63 57 61 60.3333333333
15 53 55 51 53
16 42 45 40 42.3333333333
17 32 34 30 32
18 27 27 27 27
19 27 27 27 27
20 27 27 27 27
21 27 27 27 27
22 27 27 27 27
23 27 27 27 27
24 27 27 27 27


Readings were taken starting on the 16th of Malachite (official calendar). Bandit attacks occurred on hour 9 of the 16th, hour 15 of the 17th, and hour 9 of the 18th. The temperature data looks similar to the ocean biome data, but the temperature plateaus are closer in length. Both regions reached maximum temperature 8 hours after dawn, but the desert stayed at max temperature one hour longer than the ocean did. The cooling period took the same number of hours in both regions, so the ocean biome had to spend longer at the low temperature plateau. Is the difference between the temperature curves due to biome or to latitude? More measurements will tell.

By the way, the ocean measurements were taken on the 11th and 12th of Malachite (official calendar).

[wierd]

The lack of a sinusoid over the desert is practically impossible to handwave away. Either the atmosphere has some bizarre polarization effect going on, or the temperature modeling is simply broken. 

In this case, i'd say the temperature model is broken.

This means using it as originally planned is ...... now rather complicated.

[itg]

I'm not sure it's all that weird. If you'd ever lived in the desert, you'd know the temperature really does tend to plateau in the afternoons. Take a look at this hour-by-hour data from June 16th in Phoenix, AZ. Take a look at some of the surrounding days, too. The graphs aren't nearly as regular as the DF graphs, but there's a clear tendency to heat up to about 105° F and hang there for around 6 hours. Although the night time data on the 16th of June looks more sinusoidal than flat, there are plenty of other days with clear night time plateaus, too. Like this one.

I picked these examples more or less at random, by the way. They are typical of the dozen or so dates I scanned.