New River Spreadsheet and a Note on Meanders

Ok, I said I'd make a spreadsheet to figure out the velocity of floodwaters, so here it is:

https://drive.google.com/open?id=1ywgbsL2LDHmilJcopdpemxe4GkGTVJMf

It's just a quick and dirty calculation, assuming a triangular river cross-section, and absolutely not taking into account that the slope of the riverbed at its normal height and the slope of the adjacent area might not be the same, but it'll get you close enough for game purposes.

Note that if you already know the width, depth, and slope of a river, you can use the flood calculation pages to work out the velocity; just fill in the yellow areas and the green area will be your output.  It doesn't even have to be a flooded river, just any flowing water with known parameters.  The other cells in the spreadsheet are really just intermediate calculations that I didn't bother hiding.  It's just easier that way.  Besides, this calculation is a lot more straightforward than the first two pages, so a couple of unimportant but visible cells isn't going to busy up the spreadsheet too bad.

All that said, I was going to write a post working out all the details of meandering rivers.  Meanders follow certain mathematical rules, and knowing them can help you draw more realistic rivers.  But I'm not going to, because this guy has already done it.  Thanks, Dave Richeson.

Entrenchment

Entrenchment is the last major characteristic in the Rosgen classification system. It is expressed as a ratio, giving the new width of the river if it were to be twice as deep as normal (as might happen in a 50-100 year flood).  This, not coincidentally, helps describe the immediate area surrounding the river.

The lower the entrenchment number, the deeper the river is cut into the landscape.  The higher the number, the more it lies along the general surface, spreading wider during a flood event. 

 For example, in our sample river map we've been following for the last several posts, the river in hex 0306 is ~90 feet deep, ~1950 feet across, and is type F, which is a deeply entrenched river type.  We find the entrenchment ratio is 1.2, so during a major flood event, the river in hex 0306 will be (90x2 = 180) 180 feet deep and (1950x1.2 = 2340) 2340 feet across.  The velocity should also be recalculated...I guess I should add a flood page to the spreadsheet.

Looking closer at this info we just found, you can see that if you move directly away from the river (perpendicularly), assuming that the river spreads equally to the left and right as the floodwaters rise, the land rises 90 feet (the added flood depth) in the course of 195 feet (half the added width of the floodwaters), giving the land there a slope of (90/195 = .46) .46, a very steep grade.  Tributaries flowing into the river here could easily be type Aa+ (remember that this river type isn't randomly generated in this system), although if they run in at an oblique enough angle the steep slope might be mitigated.  Also, characters will have an extra hard time crossing the river here.  As steep as the slope is, there probably isn't a road running down to the river, so no ferries or bridges either; if they have to get across the river right here, it'll mean a climb down to the river, a long swim, and then a climb back up on the other side.

Also worth mentioning, a 50 year flood, by definition, has a 2% chance of occurring in any given year, and a 100 year flood has a 1% chance.  Therefore, if you are using an annual events table to shape your campaign, there should be a 1-2% chance of needing to use the entrenchment ratio each game year...

This is the last addition to the river generation table, which is as follows:

 

Die Roll	Slope	DA	C	E	F	D	B	G	A	Aa+
1	0.0001	x	x	x	x	x				placed as needed
2	0.0003	x	x	x	x	x
3	0.0007	x	x	x	x	x
4	0.0015	x	x	x	x	x
5	0.002	x	x	x	x	x
6	0.004	x	x	x	x	x
7	0.006		x	x	x	x
8	0.01		x	x	x	x
9	0.02					x	x	x
10	0.03					x	x	x
11	0.04								x
12	0.05								x
13	0.08								x
	Sinuosity	1	Min 1.4*	Min 1.5*	Min 1.4*	1	Min1.2*	Min 1.2*	1.0 – 1.2	1.0 – 1.1
	WDR	2d20	(d10x2)+12	d12	(d10x2)+12	(d10x4)+40	(d10x2)+12	d12	d12	d12
	Entrench.	>2.2**	>2.2**	>2.2**	(d4/10)+1	1	(d8/10)+1.4	(d4/10)+1	(d4/10)+1	(d4/10)+1
* For these river types, roll 1-6 d6, divide by 10, and add 1, for a total of 1.1 to 4.6.  If this result falls under the minimum listed, use the minimum instead.
** These river types are associated with floodplains. If obvious floodplain boundaries (hills, mountains, etc) are apparent on the map, the river will fill that area during a 50-100 year flood. If boundaries are not apparent for whatever reason, the entrenchment ratio can be simulated by rolling an “exploding” d6 (ie, if a 6 is rolled on d6, keep it and add another d6, continuing to add d6s as long as 6s are rolled), dividing by 10, and adding to 2.2 (or (d6X/10)+2.2)

River Sample take 2

In the original river sample I ran, I used 50 inches of rain as the average per hex, which is a little on the high side.  In US terms, only the deep South and Pacific Northwest get that much in a year.  Thirty inches is the national average, and closer to Europe's average annual rainfall as well (although still a little high).  With that in mind, here is the river data with 30 inches of rain per hex.

hex	flow	slope	river type	wdr	sinuousity	adjusted slope	depth	width	velocity
0109	93600	0.0003	D	60	1	0.0003	25.7	1542.7	4.7
0110	156000	0.0007	E	7	1.6	0.00044	65.5	458.5	10.4
0111	234000	0.0015	DA	20	1	0.0015	40.5	810.5	14.2
0212	280800	0.0001	DA	23	1	0.0001	68	1572	5.2
0601	93600	0.0015	D	76	1	0.0015	17.4	1322.4	8.1
0602	234000	0.004	C	28	2.7	0.00148	35.8	1002	13
0603	390000	0.0003	C	20	2.1	0.00014	49.7	994.4	15.8
0604	577200	0.0003	C	16	3.1	0.000097	103.4	1653.9	6.8
0704	702000	0.0001	E	12	2.6	0.000038	147.9	1775.3	5.3
0705	795600	0.0001	E	5	1.5	0.000067	196.5	982.7	8.2
0706	873600	0.0007	E	9	2.1	0.00033	119.6	1076.2	13.6
0707	951600	0.0007	C	14	1.7	0.00041	100.1	1401.4	13.6
0103	187200	0.0001	C	16	3.1	0.000032	83.4	1334.9	3.4
0104	249600	0.0001	DA	23	1	0.0001	65	1504	5
0105	312000	0.0001	DA	34	1	0.0001	61.4	2088.3	4.9
0206	374400	0.0001	F	14	3.3	0.00003	115.2	1612.8	4
0306	405600	0.0003	F	22	1.9	0.00016	73.1	1608.2	6.9
0407	499200	0.0007	C	20	2.2	0.00032	71.9	1438.6	9.6
0507	530400	0.0001	C	28	2.3	0.000043	94.4	2644.4	4.2
0607	546000	0.0003	E	6	3.3	0.00009	150	900	8.1
0608	592800	0.0001	C	28	1.8	0.00005	95.7	2680.1	4.6
0708	1638000	0.0003	F	24	1.7	0.00018	116.8	2803.1	10
0809	1716000	0.0007	DA	33	1	0.0007	81	2695	15.5
0810	1825200	0.0015	F	22	2.8	0.00054	102.3	2250.3	15.9
0811	1965600	0.0001	DA	13	1	0.0001	176	2287	9.7
0911	2028000	0.0007	C	14	2.6	0.00027	143.8	2012.9	14
0912	2137200	0.0015	DA	27	1	0.0015	83	2240	23

These are still pretty deep and wide, supporting my earlier observation that, on a 20 mile-per-hex map at least, if a river is marked, it is a major obstacle.  Bridges, ferries, or magic are needed to get across. 

Sample River Update

Going back to the sample river I've used to illustrate my thinking throughout this river project...

I'm going to start with this small river to the west.  So far, we know this much:

hex	flow	slope
0109	156000	0.0003
0110	260000	0.0007
0111	390000	0.0015
0212	468000	0.0001

None of the slopes dictate a river type for any of these hexes, and there are no terrain types that suggest a river type, so I'll roll randomly from among the possible types (DA, C, E, F, and D), and then determine the width-to-depth ratio and adjust the slope value due to sinuousity for each hex.

hex	flow	slope	river type	wdr	sinuousity	adjusted slope
0109	156000	0.0003	E	7	1.6	0.00048
0110	260000	0.0007	D	60	1	0.0007
0111	390000	0.0015	DA	20	1	0.0015
0212	468000	0.0001	DA	23	1	0.0001

So, we can see already that this river is going to go from a relatively narrow, deep river to a wider, shallower river and dropping a bunch of sediment.  I might have to go back and change this; it doesn't make much sense to drop sediment with the slope increasing.  If anything the river should speed up and erode more. For now we'll press forward and run these values through the spreadsheet.  Since I didn't work out every possible WDR outcome for the spreadsheet, I've just used the average of the results for WDR 22 and 24 to find the results for WDR 23 in hex 0212.  For what it's worth, the only significant difference it made was in the width.

hex	flow	slope	river type	wdr	sinuousity	adjusted slope	depth	width	velocity
0109	156000	0.0003	E	7	1.6	0.00019	76.9	536.7	7.6
0110	260000	0.0007	D	60	1	0.0007	32.2	1930.6	8.4
0111	390000	0.0015	DA	20	1	0.0015	49.1	981.6	16.2
0212	468000	0.0001	DA	23	1	0.0001	82.9	1904.8	5.9

Looking at these final results, I'm going to go back and switch river types between hexes 0109 and 0110.  If the river speeds up, as it does here, there's no way for it to drop its sediment and form a type D stream in hex 0110.  Switching the two river types then gives us:
 

hex	flow	slope	river type	wdr	sinuousity	adjusted slope	depth	width	velocity
0109	156000	0.0003	D	60	1	0.0003	31.1	1868.4	5.4
0110	260000	0.0007	E	7	1.6	0.00044	79.3	555.3	11.8
0111	390000	0.0015	DA	20	1	0.0015	49.1	981.6	16.2
0212	468000	0.0001	DA	23	1	0.0001	82.9	1904.8	5.9

All right then, moving on, here is the other major river, with its two main tributaries broken out separately as before.  At this point, I have two observations: 1) type D rivers show up more often than they should, given the circumstances required for their formation (you should either move them to a better position as I did for the small river above or just reroll the river type if type D comes up in an inappropriate spot); and 2) if you have a river marked on a 20 mile hex map, its probably impassable without a boat or a bridge.

hex	flow	slope	river type	wdr	sinuousity	adjusted slope	depth	width	velocity
0601	156000	0.0015	D	76	1	0.0015	21	1601.7	9.2
0602	390000	0.004	C	28	2.7	0.00148	43.3	1213.7	15.1
0603	650000	0.0003	C	20	2.1	0.00014	92.7	1854.6	7.6
0604	962000	0.0003	C	16	3.1	0.000097	125.2	2003.1	7.8
0704	1170000	0.0001	E	12	2.6	0.000038	179.2	2150.1	6.1
0705	1326000	0.0001	E	5	1.5	0.000067	238	1190.1	9.4
0706	1456000	0.0007	E	9	2.1	0.00033	144.8	1303.5	15.4
0707	1586000	0.0007	C	14	1.7	0.00041	121.2	1697.3	15.4
0103	312000	0.0001	C	16	3.1	0.000032	101	1616.7	3.8
0104	416000	0.0001	DA	23	1	0.0001	79.3	1822.5	5.8
0105	520000	0.0001	DA	34	1	0.0001	74.3	2529.2	5.5
0206	624000	0.0001	F	14	3.3	0.00003	139.5	1953.4	4.6
0306	676000	0.0003	F	22	1.9	0.00016	88.5	1947.8	7.8
0407	832000	0.0007	C	20	2.2	0.00032	87.1	1742.3	11
0507	884000	0.0001	C	28	2.3	0.000043	114.3	3202.7	4.8
0607	910000	0.0003	E	6	3.3	0.00009	181.7	1090	9.2
0608	988000	0.0001	C	28	1.8	0.00005	115.9	3246	5.3
0708	2730000	0.0003	F	24	1.7	0.00018	141.5	3394.9	11.4
0809	2860000	0.0007	DA	33	1	0.0007	99	3266	17.7
0810	3042000	0.0015	F	22	2.8	0.00054	123.9	2725.5	18
0811	3276000	0.0001	DA	13	1	0.0001	213.6	2770.6	11.1
0911	3380000	0.0007	C	14	2.6	0.00027	174.1	2437.9	15.9
0912	3562000	0.0015	DA	27	1	0.0015	100.5	2712.2	26.2

Well, this is a pretty broad river by the time we get to the lower reaches on this map. Right around a half mile across.  This table was made using 50 inches of rain annually in each hex, which is kind of on the high side, apparently.  I'll recalculate all this with 30 inches of annual rain and see what difference it makes, leaving the river types and slopes unchanged.  But I'll do that in a later post...this one has waited too long as it is.

Excuses excuses

Well, between the holidays, out of town travel, a bout of the Captain Trips, and weather that's been too cold for normal life in this drafty old house, I haven't done anything here for a while.  That's not too unusual, I guess, since I tend to work pretty slowly churning out posts, but in this case I've worked zero for several weeks.  I'm getting back on it (although the house is still drafty, and it is still too cold for comfort), and should have a real post fairly soon.