Tropical storm, shortly after yesterday (7)

I believe the answer is:

monsoon

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'tropical storm' is the definition.
'monsoon' can be an answer for 'storm' (thesaurus). I'm not sure about the 'tropical' bit.

'shortly after yesterday' is the wordplay.
'shortly' becomes 'soon' (synonyms).
'after' means one lot of letters go next to another.
'yesterday' becomes 'mon' (I am not sure about this - if you are sure you should believe this answer much more).
'soon' after 'mon' is 'MONSOON'.

Can you help me to learn more?

(Other definitions for monsoon that I've seen before include "Rain-bringing weather feature" , "Seasonal wind (south-west or north-east) of southern Asia" , "Rainy season in southern Asia" , "Rainy period" , "Wet seasonal wind" .)

I've seen this clue in the Sydney Morning Herald.

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