# Why does the frost depth increase when the surface temperature warms up?

We've had an unusual winter this year, with a late cold snap that is causing people's underground water lines to freeze. Now that the weather has warmed up quite a bit, even more people's lines are freezing, because the frost is being pushed down even deeper by the thawing ground above it.

What causes this phenomenon? Why does the frost not simply thaw from top to bottom after it warms up? Why does it continue to go deeper?

That's is due to the slow diffusion of heat into the ground. Unlike a liquid, pieces of soil can't move around, therefore, in the absence of liquid water, heat can only be transferred by conduction, a process that follows the diffusion equations and it is very slow.

This means that if there is a heat wave, or a cold snap, their effect will reach deep layers of the soil with a delay, the deeper the longer the delay and the more dampened the wave will arrive.

This figure shows a heat wave in the soil

(figure from Soil Temperature at ScienceDirect)

As you can see, the plot shows that there was a peak in temperature of about 27°C at the surface (0m) at time t=6h, but that peak in temperature slowly diffused downwards, such that at a depth of 0.2 m, the peak happened at time t=8h reaching only about 23°C, and at a depth of 0.4 m it arrived even later, at about t=18h and reached only 21°C.

In you case, what is happening that the cold snap is still "traveling" down the ground.

An alternative way to understand this, is that the cold snap cooled the ground so that a layer below the surface can be now at, let's say -5°C, and it is on top of a deeper layer at +1°C, where the water pipe is located. What that deeper layer feels is not what happens in the surface, that is nice and warm, it feels the temperature of the layer right on top of it, that is still very cold. So that deeper layer will cool down and eventually freeze. Freezing as well the water line with it.

That said, and to address some great comments. The current freezing of underground water lines responds to a past forcing. Therefore, it have nothing to do with current weather and is not the thawing ground what pushes the frost down. It is just the normal curse of events in the propagation of a cold/hot wave down into the ground.

• Lovely explanation. With some interpretation, this also neatly explains why the seasons lag behind the attitude of the Earth in relation to the Sun; although that might be a question better asked in isolation from this one.
– Rich
Mar 19, 2019 at 19:14
• If I read your answer correctly you're saying: the deeper layers care about it being cold in the past. That it's warmed up now is just a coincidence and has nothing to do with the frost depth getting deeper; the thawing ground is not "pushing it down". Assuming I'm right it would be worth saying that explicitly Mar 19, 2019 at 22:52
• So in reality the warmer surface temperature isn't driving the frost down, there's just a delay in the time it takes for the cold to reach it's max depth? Mar 20, 2019 at 15:03
• Yes. So you have frozen soil half a meter down, it will still be warmed from the layers below (causing them to cool down) while being warmed up from the top as well. As long as there's a differential in temperatures this will continue. Mar 20, 2019 at 16:13
• @RichardTingle I added a paragraph to make that explicit. Thanks for the suggestion! Mar 20, 2019 at 21:03