4.25

My sister posted, on Facebook, that if Lake Superior were thickened and spread over the North American Continent like so much buttercream icing, we would all be kicking about in a foot of water. I have heard this fact before, but never started making connections until some Russian fellow, intent on showing the glory of his great country, casually slipped in that Baikal would cover us in 24 inches. I have since shown both of them wrong.*

For a time, all my sources were from Wikipedia, the great repository of all information that other people have not been too lazy to write down for others. I started with the list of lakes by volume (practically bookmarked; it's one of my favorite haunts). Then, of course, I needed continents by land area. Australasia/Oceania/Australia is the only complication there, and I decided for Australia (continent) because it's easy.

To spread the lakes like icing, I needed to have only their volume (km³) and the continent's area (km²). From there, it was ten agonizing minutes listening to Larry screaming about being trapped in space and to the dog chewing on a pop bottle until I figured out that all I really had to do was divide the area (km³) by the base (km²) to find the height. I had to step out of the room and I had done it in a minute and a half.

My hypothesis:

Because I have spent perhaps five hours of the last calendar year just pouring over the largest lakes in the world (Aral Sea whaaaaat), I felt fairly confident in saying that Africa would have the most lake icing. Asia is just too big, even for Baikal. That's saying something. Essentially, as long as we held ourselves to freshwater lakes, the ratio of lake size to continent size would be smallest in Africa, then Asia, then North America.

My findings:

Baikal (23,600 km³) spread over Asia (43,820,000 km²) would be 53.8 cm or 21.2 inches.
Tanganyika (18,900 km³) spread over Africa (30,370,000 km²) would be 62.2 cm or 24.5 inches.
Superior (11,600 km³) spread over North America (24,490,000 km²) would be 47.4 cm or 18.7 inches.
Titicaca (893 km³) spread over South America (17,840,000 km²) would be 5.006 cm or 1.97 inches.
Vostok (5,400 km³ ±1,600) spread over Antarctica (13,720,000 km²) would be 39.4 cm or 15.5 inches. (The 1,600 km³ variance results in extremely inaccurate estimates, but Antarctica's icing would be between 51cm/20in and 28cm/11in.)
Ladoga (908 km³) spread over Europe (10,180,000 km²) would be 8.9 cm or 3.5 inches.
Te Anau (?) spread over Australia (9,008,500 km²) would be something, I'm sure. Small, is what.

My hypothesis is upheld, and pleasantly, too. The largest freshwater lakes in the world follow the sizes of their continents exactly for the first three in both categories. Africa takes the icing depth . . . cake . . . with a resounding 3 inch margin. Sadly, I could almost forgive the roughly 11 km³  difference reversing the size-to-size list in for Europe and South America, but Vostok I cannot forgive. And what's the deal, Te Anau? You're supposedly the largest lake in your continent, but nobody knows how large you are?

My personal hell:

I said that "for a time" all sources were Wikiped, but Te Anau ran me into a wall. All I'm told is its length, surface area, and maximum depth. Even the Kiwi government let me down with only the 1966 "Encyclopaedia of New Zealand," a document I'm sure is fascinating, but is unhelpful here. However, I quickly found out why.

Te Anau is a lake created by glacial action (so is Superior--impressive when you know that Baikal and Tanganyika are holes where the Earth has split and Superior's just a scoop but it still holds its own). However many years ago, a huge wall of ice came through and carved out a valley for Te Anau to sit in. As the dumb thing melted, its leavings, all piled up at the front end, created a natural dam to hold the water. Even though something like eight rivers feed Te Anau, only one is left as it drains. I still couldn't quite understand why nobody knew the depth, though.

Te Anau floods.

That's why it's so difficult to measure exactly how deep the lake is. It's not a major artery for commerce because the moirane keeps passage difficult, and besides, the Waiau River is no St. Lawrence. No large boats are coming up and there's no need to measure the depth of the lake any time soon. I found a paper proposing that the New Zealand government dam up the lake and use it for hydroelectric power, cutting it off from downstream boat traffic. That's where I learned that Te Anau floods by up to four meters or thirteen feet (pg 4). So what's a boy to do?
I found a list of moirane-dammed lakes (six on the South Island alone!) and I'm going to compare them, numerically, to determine some sort of rough relationship between surface area, depth, and volume. When I get a constant, I'll maybe be able to estimate Te Anau's size. My lowest possible volume is Lake Taupo at 59 km³, formed by an entirely different mechanism, but supposedly smaller in volume. My highest possible volume is where the list of largest lakes terminates: Lake Nicaragua at 108km³.

Lake	Surface (km2)	Average/Max Depth (m)	Volume (km3)
Oahu	54	74/129	4.02
Pukaki	178.7	47/70	4.66
Tekapo	84.5 ±2.5	69/120	6
Wakatipu	289	230/380	?
Te Anau	344	?/417	????

You can already see that the average depth of a moirane-dammed glacial lake is roughly 0.6 its maximum depth.
average depth:maximum depth
O0.57, P0.67, T0.57, and W0.61. Wakatipu is excellent for us because it's deep like our lake and almost the same size. With that ratio to estimate, Te Anau's average depth is 250m. Working by a ratio of surface area to average depth, we see less regularity in the ratios.
surface area: average depth
O0.72, P3.8, T1.2, W1.3. I think Oahu is too thin and Pukaki too flat for our use because averaging the ratios gives me 1.8. Throw them out. Te Anau's surfacearea:average depth is 1.37. Again, Wakatipu to the rescue as our type/antitype. Finally, we have to figure out volumes. I'm going to throw out Pukaki again for surface area when I calculate averages.

surface area:volume
O13.4, P38.3, T14.1, W? (avg 13.75)

average depth:volume
O18.4, P10.1, T11.5, W? (avg 13.3)

I'm pleased with the ratios, because Tekapo and Wakatipu have had a positive correlation throughout, and Wakatipu is very similar to our lake. Remembering that Te Anau > Taupo, the largest km² freshwater lake on the continent, I can now plug Te Anau's estimations into the ratios we've developed.

344 km² / 13.75 = 25.0 km³
250 m / 13.3 = 18.8 km³

Well, darn. I had such a high calculating all of that up until thirty seconds ago when I scrolled up to see that the smaller lake is 59 km³. Obviously, ratios have carried us as far as they can. It's time to start treating these lakes like cubes.

average depth*surface area
O4.00, P8.40, T5.83, W66.47
reported volume
O4.02, P4.66, T6.00, W?
Considering that Pukaki is a freak of nature, I think these other lakes probably are cubes. Since Wakatipu is our comparison and our estimate shows it already bigger than Taupo, our lowest possible volume, I think it's safe to say that I can now reveal my findings:

Te Anau volume: 86 km³

If you thickened Te Anau and spread it over the continent of Australia/Australasia/Oceania, you would have a resultant depth of 0.9547 cm or 0.3758 in. In actual terms, that's 4/5 a coffee bean or 6/5 a grain of rice, or half a penny stood on end (1.002r). It's almost exactly one Lego brick (0.994). I challenge you to find a Lego or a penny in your house and put it on the ground and look at it. I practically demand that you do, if only to remind you that if it rained over the entirety of that continent as hard as it did in Barot, Guadaloupe on 26th November 1970, it would have rained the entire contents of Te Anau in fifteen seconds.

*Baikal would bury North America in 37.94 inches, enough to easily drown all 10 of the shortest humans of all time. I think Warwick Davis would make it.

*Baikal spread over the entire planet is 4.63 cm or 1.82 in.

This post took 4.5 hours from 9:27am to write. I used two sheets of notebook paper, roughly twenty five open tabs in Chrome, and forgot to eat breakfast.