There is the possibility that an adverbial phrase modifies an entire clause. There is also the possibility that a prepositional phrase is adjectival rather than adverbial.
The weather during summer can be very hot in Libya.
Here, there seems little room for argument. "During summer" modifies "weather" or "the weather". In either case, it is an adjectival prepositional phrase.
During summer, the weather can be very hot in Libya.
Here, there seems to be plenty of room for argument. This clause makes sense regardless of whether we consider the prepositional phrase to be supplemental, modifying the entire following clause; or adjunctive, modifying only the verb "can be". Either case can be labeled adverbial.
The weather can be very hot in Libya during summer.
There is nothing but room for argument here. "During summer" could modify "Libya", "very hot", or "can be". In this example I prefer to interpret it as modifying the verb, but the other interpretations are far from senseless.
The weather can be very hot during summer in Libya.
For this example I cannot even establish that "during summer" is the complete prepositional phrase. Both [ [during summer] [in Lybia] ] and [ during [ summer in Lybia ] ] are sensible ways to parse the phrasing.
The entire adjective phrase "very hot during summer in Lybia", regardless of its internal structure, is the complement of the subject "the weather". I cannot support the notion that "in Lybia" on its own in any way modifies "the weather" in this sentence.
These ambiguities do not represent a flaw in the English language. Instead, they are a feature of it. The overall meaning of this particular sentence does not change, regardless of the exact role that the prepositional phrase plays or the particular position which it takes.
It is easy enough to construct a sentence in which an ambiguity results in more than one possible overall meaning:
We are not discussing Libya's weather during the summer.
In this case, "during the summer" might modify "Libya's weather" or it might modify "are (not) discussing". Under the former interpretation, we are discussing something other than Libya's summertime weather. Under the latter, the discussion about Libya's weather happens during some other season if it happens at all. The former interpretation considers the prepositional phrase in an adjectival role, while the latter considers it adverbial.