long rainy spell
霖 centers on a prolonged, continuous rain: a long rainy spell that lasts for days.
霖 combines 雨 (rain) with 林 (forest), suggesting rain falling continuously on a forest, evoking a long-lasting rain.
Rain 雨 falling on a forest 林 for days without stopping: that's a long rainy spell.
For リン, imagine a long rainy spell making the forest glisten like a ring of water: ring -> リン.