Hills that split the three

A small atlas of America’s drainage triple junctions

A friend named Steven sent me a question last week. It turned out to be exactly the kind of thing the data pipeline I’ve been building for Kentucky already knew how to answer, so I answered it. While I was at it, I noticed the answer belonged to a small family of points scattered across the continent. So I made this.

Steven’s question, in his words:

“Where is the Purchase area’s ‘continental divide’? Marshall, Calloway, and some of McCracken all have creeks that flow east towards the Tennessee River. Fulton, Hickman, Carlisle, and Ballard flow east or north to the Mississippi or Ohio. I think most of Graves flows west into Mayfield Creek, but some goes into Clark’s River, right? Somewhere, there’s a hill that splits the three and that’s really interesting to me.”— Steven P.

He looked at maps and called Wice Church Road, between St. John’s and Boaz, as the line. The actual hill turned out to be a 494-foot saddle about 2 km south, on St John Church Road. Same community he was reading, the next church-named road over. The math triple-point sits 9 m from the centerline.

Once you can ask “where does a raindrop landing here end up” for one point, you can ask it for ten thousand. What comes back is a whole geometry. Mathematicians have a name for the kind of point Steven was asking about: a monkey saddle. A degenerate critical point of the elevation surface where three valleys descend and three ridges climb, alternating around a single point at which the gradient vanishes and the Hessian’s determinant goes to zero. They’re measure zero in the space of smooth surfaces, and only exist when the landscape happens to align just so. A few of them are famous.

Triple Divide Peak — Glacier National Park, Montana

The most famous one. Pacific Ocean, Hudson Bay, Gulf of America. The only true three-ocean point in the contiguous United States. Marked, signed, hiked by tourists in late summer. Its three slopes water three different polar oceans.

The Laurentian triple — northern Minnesota, near Hibbing

Three rivers leave it: one heads east to the Atlantic via the Great Lakes and the St. Lawrence, one heads north to Hudson Bay via the Red River, one heads south to the Gulf of Mexico via the Mississippi. Sits on the Laurentian Divide near the Mesabi Iron Range.

Triple Divide — Potter County, Pennsylvania

The Appalachian one. Two of its three slopes reach the Atlantic, but they take wildly different routes: one via Chesapeake Bay (the Susquehanna), one via the St. Lawrence (the Genesee). The third slope drains west into the Allegheny and on to the Gulf via the Ohio and the Mississippi.

McCracken County — Paducah, Kentucky

The local one, and sub-continental: all three drainages end up in the Mississippi at New Madrid, less than 60 river-miles downstream. Mathematically the same beast. The 494-foot hayfield Steven was asking about.

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

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