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How Long Does a Drop of Water Take From Lake Superior to Lake Erie?

Timing a continental water system with a hydrography dataset: river travel times computed from NHDPlus HR flow and velocity, lake residence times as volume divided by outflow, and why the Great Lakes hold what enters them for centuries. Includes the Lake Michigan route through the Straits of Mackinac.

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Transcript

Drop a raindrop into Lake Superior. How long before that water reaches Lake Erie? Days? Months? It is one of the most surprising numbers in hydrology — and you can compute most of it from a single national dataset.

First, the route. Out of Lake Superior through the St. Marys River. Down the length of Lake Huron. Through the St. Clair River into little Lake St. Clair, then down the Detroit River, and into Lake Erie. Notice something about this thousand-kilometer journey: only about two hundred kilometers of it is actual river. The rest is lake. Hold that thought.

The rivers we can compute directly. The National Hydrography Dataset carries, for every mapped channel in the country, an estimated mean flow and velocity. Reading our archive: the St. Marys runs ninety five kilometers at about zero point seven meters per second, carrying twenty three hundred cubic meters every second — one point six days. The St. Clair: fifty eight kilometers, six thousand cubic meters per second — under a day. The Detroit: forty eight kilometers — another two thirds of a day. Every river on the route, end to end: about three days.

But a lake is not a river. Water entering a lake mixes into a volume that drains slowly, and the average delay is simple division: volume over outflow. Lake Superior holds twelve thousand one hundred cubic kilometers, and its outflow is that same twenty three hundred cubic meters per second we measured in the St. Marys. Divide, and you get roughly a hundred and seventy years. Lake Huron: three and a half thousand cubic kilometers — about nineteen years. Lake St. Clair, small and shallow: six days.

Now stack the whole journey. Rivers: three days. Lake St. Clair: six days. Lake Huron: nineteen years. Lake Superior: a hundred and seventy.

In total, an average drop takes roughly one hundred and ninety years to travel from Lake Superior to Lake Erie — about two centuries.

The rivers — the only part you can actually watch flowing — account for five thousandths of one percent of the trip.

And what if the drop starts in Lake Michigan instead? Michigan has no outlet river at all. It drains through the Straits of Mackinac — about eight kilometers wide — where the hydrography archive reads roughly fifteen hundred cubic meters per second flowing into Huron. The two lakes stand at the same water level; hydraulically, they are one system. So: four thousand nine hundred twenty cubic kilometers, divided by that flow — about a hundred years. Add Huron and the rivers, and a drop from Lake Michigan reaches Erie in roughly one hundred twenty years. Faster than from Superior — but only by decades.

One honest caveat: that is an average, and the distribution around it is enormous.

A drop that stays near the outlet current can make the trip in a few years. A drop that mixes into Superior's deep basins can wait five hundred. And many drops never make the trip at all — they leave by evaporation instead. But the average carries the message that matters: whatever enters Lake Superior today, the Great Lakes will remember for centuries.

A continental water system, timed with a hydrography dataset and long division. The river is the fast part — the lakes are the memory. And both are physics you can compute.

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