Is there an expression for an abrupt change in height? I’m looking for a word for the edge of the change, like in the German word Geländekante.
A cliff or precipice is at the boundary to an abrupt change in altitude.
a steep rock face, especially at the edge of the sea.
synonyms: precipice, rock face, crag, bluff, ridge, escarpment, scar,
I don't speak German, but looking at this page it seems to me Geländekante can apply to any abrupt change in "level".
Those examples range from "height discontinuities" of hundreds/thousands of feet (cliffs, Ayers Rock) to mere inches (kerb between road and pavement, small mismatch in a loading bay area). So I think the short answer is there is no equivalent "generic" word or common expression for this in English.
1: At the "geological" level there are lots of terms (cliff, escarpment, bluff, etc.), with the same or overlapping meanings.
2: Somewhere in the middle - usually from the "above" perspective, with emphasis on the danger of falling over the edge - are terms like precipice, drop.
3: At smaller scales (the most likely context where you'd need a more general-purpose term) the best bet is probably step (Mind the step = Don't trip over the upcoming small change in level).
If you are specifically referring to a change in height of a person (a human) - then we call that a "spurt", or more specifically a "growth spurt" - when a child grows inches taller, almost overnight.
There are dozens of words for these things that vary in aspect, specificity, origin, and region. Sometimes they emphasize the vertical aspect; other times the line at the top or bottom. Some are for collections of these things; others for singular instances.
- combs ridge
- castle rock
Some of these terms are common and general; others rare and specific. There are many more. Some are found in every dictionary; others only in specialty lexicons devoted to geography. One of the latter can be found at the web site Home Ground: Language for an American Landscape.
Scarp, or escarpment. Wikipedia:
- Cliff, a significant vertical, or near vertical, rock exposure
- Escarpment, a steep slope or long rock that occurs from erosion or faulting and separates two relatively level areas of differing elevations
Some comments clarified that the context is terrain.
In this case, you could say The road (or path, or ground, or whatever) dropped off sharply OR rose sharply. If you google these phrases, you'll see they're extremely common.
(Next time, could you provide the context in your question, please?)