big rain, long rainy spell
霈 centers on heavy, sustained rain: a downpour or a long rainy spell that soaks everything.
霈 combines 雨 (rain) with 沛, which likely contributes the sound and the idea of abundance or copiousness, together suggesting heavy, plentiful rain.
Rain 雨 pours down in abundance 沛, creating a scene of big rain and a long rainy spell.
For ハイ, imagine a heavy rain that makes everyone say 'Hi!' as they rush for cover: Hi -> ハイ, and the rain keeps falling.