Melting glaciers. Rising sea levels. Drowning cities. A disaster is coming our way!
Is that proper grammar?
Yes, indeed. Sentence fragments. Verb implied. Punchy impact. Often overused. Still grammatical.
The first three statements are sentence fragments, not sentences. They are understandable, but are only "grammatically approved" as headlines, or as parts of a list.
Melting glaciers. Rising sea levels. Drowning cities.
For example, the following sentence is grammatically correct. Unfortunately, it is not as "punchy" as the original example:
Melting glaciers, rising sea levels, and drowning cities are signs of impending doom.
The fragments can also be converted into grammatically correct sentences:
Glaciers melt. Sea levels rise. Cities drown.
The last sentence is a grammatically complete sentence:
A disaster is coming our way!