With difficulty pick up area in depression (5)

I believe the answer is:
glean
'with difficulty pick up area in depression' is the definition.
I can't judge whether this definition defines the answer.
'up area in depression' is the wordplay.
'up area' becomes 'a' (maths abbreviation. I am not sure about the 'up' bit.).
'in' is an insertion indicator.
'depression' becomes 'glen' (glen is a kind of depression).
'a' going inside 'glen' is 'GLEAN'.
Can you help me to learn more?
(Other definitions for glean that I've seen before include "Gather; collect gradually" , "Angle (anag.)" , "Collect gradually (from various sources)" , "Pick up (information)" , "Gather remnants of corn" .)
