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It looks like there'll be a storm soon.
Literal
Near future [locative-に] storm [locative-に] become [it seems-そうだ].
A weather prediction. 近いうち (ちかいうち) 'in the near future, soon' is a set phrase. ~そうだ ('seems/looks like X') attached to the 連用形 (stem form) of a verb is the evidential 'seems to' — different from ~そうだ attached to plain form, which means 'I hear that X'. Here 'なりそう' is stem of なる + そう = 'looks like it'll become'.