How Fast Does Ice Grow? Freezing Degree Days and Stefan's Law

Short answer: ice grows with the square root of how much cold has piled up. Cold is counted in freezing degree days. A freezing degree day is 32 minus the day's average air temperature, in degrees F. Add them up and you get accumulated freezing degree days. The Army's Cold Regions lab (CRREL) estimates ice thickness in inches as a coefficient times the square root of that total. The coefficient is usually 0.3 to 0.6. At 0.6, CRREL says 300 accumulated freezing degree days make about 10 inches of sheet ice.

Growth is fast at first, then slows. The first inch comes quick. Going from 10 inches to 11 takes far more cold than going from 1 to 2. Snow on top slows it more.

No ice is ever 100% safe. Check it yourself. A formula is an estimate. Iceline's 10-day growth forecast is also an estimate. Drill a hole and measure before you step out.

What is a freezing degree day?

It is a simple count of how cold a day was. NOAA's National Weather Service Alaska-Pacific River Forecast Center computes it as 32 minus the daily average temperature (FDD = 32 minus Ta). CRREL says the running total does not begin accumulating until the first sustained period of cold temperatures.

Worked example, degrees F. Say the high is 22 and the low is 12.

• Average: (22 + 12) / 2 = 17.
• Freezing degree days: 32 minus 17 = 15.

Now run five days just like that. That is 5 x 15 = 75 accumulated freezing degree days.

Stefan's law, the plain version

CRREL's technical note on estimating ice thickness gives the modified Stefan equation as: thickness in inches = C x (accumulated freezing degree days) to the 0.5 power. The 0.5 power is the square root. CRREL says C usually falls between 0.3 and 0.6, with accumulated degree days in degrees F.

CRREL also lists coefficients by setting:

Run our 75 accumulated freezing degree days through it. The square root of 75 is about 8.7. At C = 0.5 that is about 4.3 inches. At C = 0.7 it is about 6.1 inches. (That arithmetic is ours, using CRREL's coefficients. It is a range, not a promise.)

CRREL's own example: with a coefficient of 0.6, 300 accumulated freezing degree days predict a 10-inch sheet.

Notice what the square root does. Four times the cold only doubles the thickness. That is why a bitter week in December does not double what you had in a mild one.

How snow cover slows growth

CRREL says snow on top of the ice insulates it, cuts heat transfer, and effectively lowers the coefficient. The Minnesota DNR says the same thing in plain words: the insulating effect of snow slows the freezing process. It also notes the extra weight reduces how much the ice sheet can support.

So a lake that got hit with an early dump of snow can sit thin while the air is cold. Check any snow-covered ice with a drill, not with your eyes. See also first ice and how to read it.

CRREL adds that if growth is affected by underturning, shoving or frazil deposition, the coefficient should be raised. In other words, conditions on the water can make ice thicker than the simple math says.

Why clear ice is stronger than white ice

The Minnesota DNR says clear ice, sometimes called blue ice, is the strongest and safest. It typically forms at the start of the season on top of calm water. It looks clear, but it can read blue or black when you look down into the water. The DNR says it has large crystals and few or no oxygen bubbles, which makes it very solid.

White ice forms when snow melts on top of the sheet and refreezes. The DNR says it is only about half as strong as new, clear ice because it is full of air bubbles and made of smaller crystals. Its rule: double the standard thickness guidelines on white ice. When you drill, look at the core. The DNR points out you should see how much of it is clear and how much is white. Our ice thickness chart guide has the numbers.

Why thickness changes across one lake

The Minnesota DNR says temperature, snow cover, currents, springs and rough fish all affect how safe the ice is. It also says ice is seldom the same thickness over a single body of water, and can be two feet thick in one place and one inch thick a few yards away.

The DNR names these spots as risky:

• Flowing water: streams, under bridges, culverts.
• Stream inlets: where gas holes are more likely, because vegetation and debris collect there.
• Near logs, rocks, bridges and docks: anything that absorbs sun heat can have thinner ice or open water near it.
• Close to shore late in the season: shallow water and plants warm faster there.
• Where fish or waterfowl bunch up: moving fish can bring up warm water from the bottom, and groups of geese or swans can thin patches.

Pressure ridges are different. The DNR says they come from ice contracting and expanding as air temperature swings. Ridges often have thin or flooded ice on the sheet that got pushed under, and some are hidden by snow. Read more in pressure ridges, cracks and slush.

Why a forecast never replaces a drill

Stefan's law is built from air temperature and a coefficient. It does not know about the spring under your hole, the creek mouth, the snow drift, or the ridge you drove over this morning. Even CRREL's own coefficient range is wide: 0.3 to 0.6 is a factor of two. The Minnesota DNR says it does not measure ice thickness on Minnesota lakes and that your safety is your responsibility.

Use a forecast to decide when to start looking, and use a drill to decide where to stand. Drill, measure, and keep measuring as you move.

Iceline's 10-day growth forecast

Iceline's 10-day ice growth forecast is an estimate. It is a planning tool. It is not a thickness reading and not a safety call. Use it to see when a lake might lock up, then confirm on the ice. For the temperature side, NOAA's National Operational Hydrologic Remote Sensing Center posts accumulated freezing degree day maps calculated from NOAA analysis and forecast model data.

FAQ

How many freezing degree days does it take to make safe ice?

There is no single number. Using CRREL's formula, 300 accumulated freezing degree days at a coefficient of 0.6 gives about 10 inches. Real ice varies. Measure it.

How fast does ice grow per day?

It depends on the cold and on how thick the ice already is. Thin ice grows faster than thick ice because the square root flattens out. Snow on top slows it.

Is black ice safe?

Clear ice is the strongest kind, per the Minnesota DNR. But no ice is ever 100% safe. Check it yourself.

Why is white ice weaker?

The DNR says it is full of air bubbles and made of smaller crystals, so it is about half as strong as new, clear ice.

Can I use the formula to decide if a lake is ready?

Use it to guess when to go look. Then drill.