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Storm-tide = expected high tide + storm surge (low barometric pressure/onshore winds) + wave set-up in the surf zone. Final inundation height = storm tide + wave run-up.
The inundation height resulting from a coastal storm is the sum of the storm tide height plus wave run-up, making allowance for wave set-up that occurs landward of the surf zone. The storm tide height is the sum of the expected high tide, plus the storm surge (the result of low barometric and onshore winds) plus wave set-up.