A peak, not a saddle

The Apex at Barkley Canal

Critical points of a smooth elevation surface come in three Morse-theoretic flavors. Peaks: gradient vanishes, Hessian negative-definite, water radiates outward in every direction. Pits: gradient vanishes, Hessian positive-definite, water collects from every direction. Saddles: gradient vanishes, eigenvalues of opposite sign, water flows in along two axes and out along the perpendicular two. On a generic landscape these are the only three kinds; degenerate critical points — where a higher-order term replaces the quadratic and the Hessian determinant itself goes to zero — are measure zero in the space of smooth surfaces.

Monkey saddles are the degenerate special case the catalog enumerates: three valleys and three ridges spiraling alternately around a single point at which both the gradient and the Hessian determinant vanish. They’re measure zero, they only exist when the landscape happens to align just so, and there are four of them in the contiguous United States.

This page is about a different kind of triple-drainage point. Not a degenerate saddle. A perfectly ordinary peak — Hessian negative-definite, no funny higher-order terms — that nonetheless does the same job, three meaningfully distinct downstream destinations from one footstep, because of an act of engineering.

“There’s gotta be a saddle point at the LBL canal. One drop falls into the canal, the other into Lake Barkley, the other into Kentucky Lake. Maybe not. Check me.”— a friend, idly, over text

The canal in question is the Barkley Canal — 1.75 miles, cut through the Cumberland-Tennessee divide in 1966 by the U.S. Army Corps of Engineers to connect Lake Barkley (Cumberland River) and Kentucky Lake (Tennessee River) at a uniform 359-foot normal pool. The friend’s intuition: where the canal cuts the divide there must once have been a saddle, and on the bank of the cut there ought still to be a triple-drainage point — one drop, three destinations.

The intuition is geomorphologically sound. The Morse-theoretic answer is more interesting than the question presumes.

The point — Lyon County, Kentucky

From that exact pixel the four cardinal slopes drop away in every direction:

loading…↑ Barkley Canal→ Lake Barkley↓ LBL interior← Kentucky Lake

One footstep, three meaningfully distinct downstream destinations. The north slope drops straight into the Barkley Canal, which sits at the design-uniform 359 ft normal pool of both lakes and communicates freely with each. The east slope reaches Lake Barkley (Cumberland River basin). The west slope reaches Kentucky Lake (Tennessee River basin). The south slope continues down the LBL spine and eventually rejoins one of them.

Why it’s a peak, not a saddle

A pure monkey saddle — the kind catalogued on the other page — has gradient zero and a Hessian whose eigenvalues alternate sign. Three ridges and three valleys radiate alternating around it and the surface dips between them. This point isn’t that. Topologically it’s a peak: the gradient is zero and both Hessian eigenvalues are negative, so water radiates outward in every direction. The mathematical surface here is convex up, not a saddle at all.

The classic saddle-with-three-drainages that the question imagines did exist, very near here, until the dams arrived. Kentucky Dam impounded the Tennessee River in 1944. Barkley Dam impounded the Cumberland in 1966. Both reservoirs were brought to a uniform 359 ft normal pool by deliberate engineering choice — so they would communicate freely once a canal was cut between them — and that impoundment flooded the original low gap in the Cumberland-Tennessee divide. In 1966 the U.S. Army Corps of Engineers cut the Barkley Canal across the lowest residual ridge segment connecting the two lakes, ~1.75 miles long, exactly where engineers always cut canals: at the lowest crossing of the divide, where the earthwork is cheapest. So the canal alignment is the historic saddle. Sliced through, held at 359 ft, doing its job.

The 514-ft hilltop ~600 m south of the cut is the highest above-water point of the LBL spine that retains a triple-drainage character now that the original saddle is drowned and notched. Different topology — a peak instead of a saddle — but functionally the three-direction divergence that the original question was asking about.

How the point was found

Two independent confirmations from two completely different elevation models.

The first pass used the federal national 10-meter DEM. A small search box around the suspected area, then a hunt for the local maximum. A 514-foot hilltop emerged, 56 vertical feet above its neighbors in every cardinal direction.

The second pass used the state’s own 2-foot LiDAR derivative — a sampling resolution about 200 times finer in each dimension. Same hunt at finer grain. The peak shifted by ~5 m and refined to 514.83 ft at 37.008610° N, 88.243642° W, exactly what you expect when finer sampling finds a slightly higher pixel on a rounded hilltop.

The two passes agree within 0.4 vertical feet and 0.001 horizontal degrees. Two independent elevation models picking the same hilltop is what tells you the feature is real — not a sampling artifact, not a noise spike, just a small bump on the LBL spine that happens to sit in a topographically interesting spot.

And probably more, around here, too

Western Kentucky has a lot of these kinds of points once you start looking. The Cumberland and Tennessee rivers run roughly parallel for hundreds of miles before joining the Ohio at Smithland and Paducah respectively, and the divide between them weaves north-south through what’s now LBL. Every hilltop along that spine is at minimum a two-drainage divergence; every spot where a third minor watershed (a creek flowing into the canal or directly to the Ohio) approaches the spine becomes a three-way one. At 2-ft DEM resolution you could probably mark dozens of them just in Lyon and Trigg counties.

They go unmarked, unnamed, and unvisited because most are 514 ft above sea level on a back-of-the-peninsula spine that nobody has any reason to walk to. The water knows.

← back to the catalog of monkey saddles
← over to the McCracken triple junction (Steven’s hill, the real monkey saddle of the Jackson Purchase)

If this kind of thinking is useful for the work you’re doing, let me know →

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