Heavy rain's appearance in low Cornish river and lake (8)
I believe the answer is:
downfall
'heavy rain's' is the definition.
(I've seen this before)
'low cornish river and lake' is the wordplay.
'low' becomes 'down' (similar in meaning).
'cornish river' becomes 'fal' (River Fal).
'and' is a charade indicator (letters next to each other).
'lake' becomes 'L' (geographical abbreviation).
'down'+'fal'+'l'='DOWNFALL'
'appearance in' acts as a link.
(Other definitions for downfall that I've seen before include "state of ruin" , "(Cause of) ruin" , "burst of rain" , "Ruin, humiliation" , "Ruin; heavy shower" .)