Using 'is' in your question above seems to me ungrammatical.
I agree with you, Ahmed. There is an implicit main verb "is" that joins the subject "the area of forest" (I prefer "the forest area") with its adjectival complement "larger." The "is" before "destroyed" is a dependent verb and should be understood as forming part of a relative clause. Therefore, the sentence:
- As the forest area that is destroyed is larger, natural disasters occur more frequently.
can be transformed into this parallel comparative structure in which the main verb "is" will tend to be omitted (as is usually the case with the verb "be" in these structures):
- The larger the forest area that is destroyed (is), the more frequently natural disasters occur.
What we compare, Novice, is the large size of the forest area that is destroyed with the frequency of occurrence of natural disasters. If we want to compare the degree or extent of forest destruction with the frequency of natural disasters, then a comparative adverb that refers to "be destroyed" (rather than the comparative adjective "larger") will have to be used:
- The more the forest area is destroyed, the more frequently natural disasters occur.