# "steep slope" when cold fronts encounter warm fronts: Confusing sentence in textbook

I'm currently reading a university textbook on processes that result in rainfall events. In the current processes, I'm reading there is a cold front that basically pushes warm air upwards which results in pretty heavy rain. A little before that, the process that a warm front basically moves above cold air which results in winter rain with a long duration. In the textbook I find the following sentences:

Typically, cold fronts have relatively steep slopes, about 1 in 30 to 40, while warm fronts have slopes of 1 in 60 to 120; thus precipitation is usually more intense and areally more concentrated at cold fronts than at warm fronts.

What means "1 in 30"? Could it be 1/30 = 0.0333 = 3.3% ? 1 in 60 = 1/60 = 0.016666 = 1.7%.

That would result in a steeper slope for cold fronts. Is my understanding correct? Is a 2-3% slope for warm air pushed by cold fronts realistic?

• You are correct, a slope of 1 in 30 means for a vertical rise of 1 there is a horizontal distance of 30. As you state, 1 in 30 (or 1:30) is 1/30 = 0.0333 = 3.3%, or arctan(0.0333) = 1.909 degrees.
– Fred
Commented Mar 16, 2020 at 5:25

The slope is the ratio of the vertical to horizontal distance.

From here

"Warm fronts have a gentler slope and generally move more slowly than cold fronts, so the rising motion along warm fronts is much more gradual."

You can see the steep slope of a cold front visualized,

and a more gradual slope for the warm front:

But depending on the source, there seems to be varying definitions of what the slope value actually is. It makes sense, given that the answer would be different depending on how deep you go into the front and there would be seasonal variability.

This site has a nice example:

"The cold front is steepest in the lowest several hundred meters of the atmosphere with a slope of about 1/100, meaning that elevation increases about 1 kilometer for every 100 kilometers of horizontal distance from the surface front. Then the upward slant relaxes into a much more gentle slope (e.g. 1/300). All along the upward slant of the cold wedge, cold air abuts with warmer air, creating an upward-slanting boundary characterized by large temperature contrasts."