Say you are on the shore of an arbitrary lake in the world, and you want to predict its likely depth. What do you consider?
In terms of data, you have whatever would be readily available to a person standing at the edge of the lake.
Is there a good heuristic to answer this question? Is there a good numerical model to answer this question?
You may as well ask if you stand on the coast of east Africa, the Arabian peninsular, Iran, west coast of India, or the southern tip of India, the west coast of Sumatra, the east coast of Madagascar, the Kerguelen Islands, the Maladives, Diego Garcia, or the west coast of Australia, how deep is the Indian Ocean?
Estimating the depth of a body of water from its nearby topographical features is impossible.
What distinguishes Lake Baikal, in Russia, from the great lakes of North America or Lake Victoria in Africa, or the Caspian Sea? The topographical features around Lake Baikal are not extraordinary and they give no hint as to the depth of Lake Baikal; yet it has a maximum depth of 1642 m and an average depth of 744 m. It is the deepest lake in the world.
What makes Lake Baikal so deep is it is a rift valley lake. The lake is associated with a rift valley that is pulling that part of the Asia apart. The same way the east African rift valley is pulling apart Africa.
Lake Malawi (Lake Nyasa), Lake Tanganyika and Lake Turkana are all lakes in the East African Rift. As with Lake Baikal, the depth of these lakes cannot be estimated from surrounding topology or size of the lakes - length, width or area.
IF (a big if) you can see enough local topography to estimate the underwater slopes, you can get some likely bounds. If the lake had filled yesterday, projecting the slopes on either side until they meet will give you an estimate for the lake depth. But the lake is almost certain to be shallower than this, because sediment would have been accumulating for (however long the lake has been around.
That's a defensible algorithm around here, where the landscape was covered by ice a few millennia ago, and lakes have been filling since the landscape was gouged more-or-less clean.
But Fred's point about tectonically controlled lakes is very true - if the lake has been around for long enough for fault movement to have a significant effect, all bets are off.
I'll add the extremely deep and highly lethal volcanic maar lakes of Cameroon to the list of "won't work here" situations.
And my local Loch Ness, even if tectonically almost inactive, is extremely overdeepened compared to it's surrounding topography.
And Loch Tay has three significantly different underwater topographies along it's length ...
In the simplest of cases, you can make an educated guess. While you're loading the reels of rope and a heavy "sinker" onto your boat to go measure. Remember that detecting "bottom" can itself be a tricky question.
