Watch out for localized heavy rain tomorrow.
The disease remains a localized outbreak.
地域的 means 'regional' in a broader sense, often referring to larger areas or regions, while 局地的 emphasizes a more limited, spot-like area.
局地的 describes something limited to a small area, the opposite of 世界的's worldwide scope.
Compound of 局地 (local area) + 的 (-like, adjectival suffix). 局地 is itself from 局 (office, limited area) and 地 (land, area).