Okay, long list of wierd things that could happen...

Comets come into atmosphere and melt leaving water and tiny dust landing.
Additional water will increase the oceans.
Water takes lots of energy to heat (in chemistry terms) so more water = more energy to maintain temperature = planet cools.
Enough water (e.g. comets landing to cause 800m sea level rise) would eventually accumulate into an ice age if the planet wasn't heated well enough.


So I'm guessing your society will probably still be stuck in the leftovers of an ice age. Atmospheric pressure is more regulated by temperature than things falling from space, but water from space will drop worldwide temperature if there is enough of it... and then change atmospheric pressure...

It's all rediculously interconnected. You want great answers, ask UN Climate Change what they know...