Every year, unusual weather is occurring in various parts of the world.

Literal

Every-year, world's various-places [at-に] abnormal's weather [subject-が] is-occurring.

世界各地 ('various places around the world') is a formal compound — 世界 + 各地 ('each/various places'). 異常な ('abnormal') pairs with 天気 ('weather') for 'unusual weather.' ~ている marks this as an ongoing current phenomenon, not a single past event.