Hello! I need some guidance or clarification regarding the units for precipitation rate or precipitation intensity (esp. for rainfall). I'm used to precipitation intensity being expressed in millimeter per hour (mm h-1), but I noticed that reanalysis data generally express precipitation intensity in kilogram per square meter per second (kg m-2 s-1) which somehow confuses me.

I've read somewhere that when converting from kg m-2 s-1 to mm h-1, the value just have to be divided by 3600. And that in terms of precipitation amount/accumulation, 1 mm of rain is equal to 1 kg m-2. I knew that it has something to do with liquid water having a density roughly equal to 1 kg L-1, but the explanations were rushed so I'm still confused on how these two units are related to each other.

So, I would like to ask: how exactly do we convert precipitation rate from kilogram per square meter per second (kg m-2 s-1) to millimeter per hour (mm h-1), and vice versa? How does the dimensional analysis for these units work out, and what is the conversion factor for this? In addition, how exactly do we also convert precipitation amount from mm to kg m-2, and vice versa?

Thank you very much in advance!