Why should the roof pitch be relevant, assuming that the rain
falls roughly vertically?

You have answered your own question really. If the rain does not fall
vertically the effective area intersected could be the "pitch" area.
See page 40 in the approved document:
http://www.planningportal.gov.uk/upl...F_ADH_2002.pdf
which also has more such figures (for UK rainfalls of course).



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R