Ink and Equations

Real science, written as stories, poems, satire and speeches

Ink and Equations

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    Why the Bottom of a Frozen Lake Stays at 4 °C

    The ice poem promised that the fish below swim on at four degrees all day. Why four, and not zero? The answer involves two forces fighting inside every drop of cold water, and a lake that flips itself over every autumn.

    Goes deeper into Ice Floats, Which Is Lucky for Fish Poetry. A poem about the one liquid that breaks the rule almost everything else obeys, and the fish that owe their winters to it.

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    The editors. “Why the Bottom of a Frozen Lake Stays at 4 °C.” Ink and Equations, Unpacked, 5 Nov 2026. /unpacked/why-the-lake-floor-stays-at-4-degrees/

    Fig. 1 Liquid water is densest at about 4 °C because two effects compete as it cools: ordinary contraction, and the growth of open, ice-like hydrogen-bonded clusters; so a cooling lake turns over until it is all at 4 °C, then colder water floats on top and freezes, while the deep water stays at 4 °C beneath the ice.

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    “Ice Floats, Which Is Lucky for Fish” ends its winter scene beneath the ice, where “the fish that hid swim on at four degrees all day”. It’s a precise line, and a strange one. The surface is frozen at zero. Why should the water at the bottom be four degrees, rather than zero, or something else? The answer is that water has its densest point not at its freezing point, like almost every other liquid, but four degrees above it, and the reason is a tug-of-war happening inside every cold drop.

    Most liquids simply contract as they cool. Their molecules move more slowly, jostle less, and pack closer together, so the liquid gets denser, all the way down to freezing, and the solid is denser still. Water does that too, at first. Cool warm water and it shrinks, steadily, just like any other liquid. That’s the first side of the tug-of-war: ordinary contraction.

    The other side is the thing the poem described in ice: water’s hydrogen bonds, which hold each molecule to four neighbours in open, six-sided rings, with empty space in the middle. In ice, that open structure is permanent. But even in liquid water, especially cold liquid water, small, short-lived clusters of molecules keep forming that same ice-like, open arrangement, lasting for tiny fractions of a second before breaking up again. The colder the water, the more of these clusters there are at any moment. And because they’re open, they take up more room.

    So as water cools, two effects fight. Slowing molecules pack closer, making the water denser. Ice-like clusters spread it out, making it less dense. Above about four degrees, contraction wins: cooler water is denser. Below about four degrees, the clusters win: cooler water expands and gets lighter. The crossover, where water is as dense as it ever gets, is at 3.98 degrees.

    Now put that in a lake, and follow it through a cold-country year. In summer, the sun warms the surface, and the warm water, being light, floats on top of cooler, denser water below. The lake is layered. In autumn, the air cools and so does the surface water. As it cools towards four degrees it gets denser than the water beneath, so it sinks, and warmer water rises to take its place, where it too is cooled. Wind helps stir it. The whole lake churns over, a process called turnover, until every part of it, top to bottom, is at about four degrees.

    Then something changes. As the surface cools below four degrees, it doesn’t sink any more. It’s now lighter than the four-degree water beneath it. So it stays at the top, cooling further, and the churning stops. The coldest water floats as a thin layer on the surface, and that’s where ice forms. Underneath, the deep water stays where the turnover left it, at about four degrees, the densest water in the lake, lying undisturbed at the bottom.

    The ice then protects it. Heat can only escape from the water below by being conducted up through the ice to the cold air above, and ice, especially with a layer of snow on top, is a decent insulator. The thicker the ice gets, the more slowly heat leaks through it, which is why lake ice thickens quickly at first and then more and more slowly. Most lakes deep enough never freeze to the bottom, however long the winter. The fish, whose bodies match the temperature of the water around them, slow down in the cold and need far less food, and spend the winter at four degrees in the dark.

    In spring, the whole thing happens in reverse. The ice melts, the surface warms towards four degrees, gets denser, sinks, and the lake turns over again, mixing nutrients from the bottom up to the surface. That spring turnover is part of why cold lakes bloom with life every spring.

    The sea plays by slightly different rules, and it’s because of salt. Dissolved salt interferes with water’s ice-like clusters and lowers the temperature at which water is densest. In ordinary sea water, it falls below the freezing point altogether. So as the sea cools, its surface water keeps getting denser and keeps sinking, all the way down to freezing, which for sea water is about minus two. The oceans don’t have a four-degree floor.

    So that line in the poem holds up. The fish don’t swim at four degrees by luck. They swim at four because water, uniquely among common liquids, is at its heaviest just above freezing, and so it builds every frozen lake upside down: coldest at the top, warmest at the bottom, and alive all winter.

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    Sources

    1. Wetzel, R. G., Limnology: Lake and River Ecosystems, 3rd edition (2001), chapters on thermal stratification
    2. Chaplin, M., "Water density", Water Structure and Science, London South Bank University

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