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[Firnagzen]

Before starting on your waterfall, read this. Best writeup of fluid dynamics in DF, with helpful flow flowcharts.

[LemmingKing]

Dig a 1 tile channel and fill it up with buckets by making it into a pond. Stack 2 pumps on top of each other so it just pulls it out and drops it back where it started.

First, use buckets? How?

Second, I am now getting very confused but the "leading water off the map" idea looks good, but is it possible for all of us to agree on one good idea?

[HideousBeing]

Yes, but that is incredibly easy, safe, quick, and therefore highly undwarfish.
Shame. 

Its good practice. Afterward you can divert a carp filled river down through your dining room and into a cistern where you can trap them and breed them so you have a place to drop goblin sieges and those pesky elven traders. Add magma somewhere in there for more fun. 

[slink]

Dig a 1 tile channel and fill it up with buckets by making it into a pond. Stack 2 pumps on top of each other so it just pulls it out and drops it back where it started.

First, use buckets? How?

Use the "i" menu to define the hole as a pit/pond.  Fiddle with the "P" selections until you get it defined as a pond needing filling.  Dwarves will rush around with buckets and fill the "pond" from some water source.

Second, I am now getting very confused but the "leading water off the map" idea looks good, but is it possible for all of us to agree on one good idea?

Why would we do that?   

[Kanddak]

I don't consider any study carried out which involves pumps to be proof of how a natural brook behaves.  The pressure-pathfinding of which you make mention comes into play when pumps are involved.

So you're arguing that pressure-pathfinding goes through brook surfaces, but falling water doesn't?

The water speading out/overflowing/piling up effect can be easily observed on waterfalls in streams and rivers, which have no brook surface tiles. It has nothing to do with brook surfaces blocking water; it has to do with the rate of water being generated by the upstream map edge exceeding the rate of water diffusing off the downstream map edge, which causes the riverbed to stay completely full of water, which allows excess water to overflow the banks, especially at waterfalls. You are seeing the effect of water on top of other water, not anything specific to brook surfaces.

Putting a layer of gratings and flooring into the path of the water falling from a brook which has a natural waterfall does not result in the degree of flooding which can be observed at the bottom.  Whatever the properties are of the surface of a brook, it does not act the same as a surface with constructed gratings.  A surface made purely of gratings should drain at least as fast as one made of floor and gratings combined.

Yes, the best existing model of water behavior would predict that there would be no difference at all between water falling through open space, through a grate, through floor bars, or through a brook surface tile.
You say they behave differently. Can you demonstrate this?

I am right this moment looking at a map with the upper level of the stream blocked off from falling onto the lower level, and the lower level merrily running at 7/7.

That is puzzling and I am deeply skeptical, having just this moment looked at a map where blocking the upper level quickly dried up the lower one. The lower level is allowed to drain and there are no other sources of water feeding it? I would love to see a map upload.

[Syff]

Some more movies.

Waterfall before tampering;  No flooding is observed.  http://mkv25.net/dfma/movie-1853-waterfall1
Upper portion dammed;  Lower portion mysteriously remains filled.  http://mkv25.net/dfma/movie-1854-waterfall2
Channel dug to test lower portion as water source;  http://mkv25.net/dfma/movie-1855-waterfall3
Mystery water source disabled;  http://mkv25.net/dfma/movie-1856-waterfall4
Upper portion undammed;  Lower portion is refilled.  http://mkv25.net/dfma/movie-1857-waterfall5

With or without pumps, brook tiles act akin to grates.
Separated sections of brooks providing their own water source is certainly very interesting, but as far as I can tell, unrelated.

[Firnagzen]

Interesting. It appears that the tiles being unrevealed is responsible for them acting as water sources.

You've heard of the trick, whereby if you cave in a brook surface, such that it rests on unrevealed rock (the z-level below it is unrevealed), the brook tiles will act as infinite drains, yes? But if you reveal that area below the brook surface tile, it will stop draining the water. I suspect similarly glitchy behaviour is at work here; exactly what, I'm not sure, though.

[slink]

I was busily preparing an "after" save to go with my "before" save, since I have no interest in actually playing with a dammed brook, when I saw that someone else has supplied movies of the same sort of situation.  Good, that saves me the trouble.

I believe that brooks only have waterfalls leading into another brook where there is a biome change.  The source of both the upper and lower sections is just outside the biome area of the brook section.  For a brook starting at the edge of the map, these tiles cannot be designated for digging and therefore a normal brook cannot have its water supply destroyed in the same fashion as one that originates at a biome boundary.

Digging into a dry brook from the side requires that stone be removed from the apparently empty area before a wall can be built.  This wall will then be Inside, Dark, Subterranean even though the apparently empty brook tiles were Outside, Light, Aboveground.  I have run into a glitch before, where simply designating digging in a section of brook changed that section to Inside, Dark, Subterranean, but only after some combination of actions which possibly includes saving the game but not only that. 

The four tiles I had dug out of the brook which I had intended to upload, before I saw that someone had already demonstrated my point, were andesite.  Andesite is the rock at the edge of the map where that brook section originates.  The area surrounding the four tiles is black sand, and the closest rock is alunite.  It seems that the entire brook is assumed to be made of the same rock as the edge from which it originates, once the water is removed, even though the rock is invisible.

I think it would be fair to say that brook programming seems to be outside the norm as compared to digging a ditch, filling it with water, and covering it with grates.