I'm designing planets of varying atmospheric pressures. How would increasing (or decreasing) global atmospheric pressure affect the amount/frequency of precipitation over a planet?
On Earth, low atmospheric pressure is tied to rain and storms. Lighter air is moving upward vertically, carrying moisture to higher altitudes where it can condense into clouds and rain. High pressure is linked to calmer weather. Increasing air pressure means that it will take more energy to move the greater mass of air. A thicker atmosphere can hold more moisture. Twice as much air can hold twice as much water vapor. The overall relative humidity is the same, but the volume of air is increased, which increases the amount of total humidity which can condense and fall as rain.
So, if higher pressure tends to mean calmer weather, increasing atmospheric pressure would create a planet with more stable weather patterns. However, when it does rain, snow, or storm, the amount of precipitation will be increased. This will also cause larger, albeit less frequent, thunderstorms. Some of this also depends upon factors such as planetary rotation and the intensity of sunlight. Faster rotation means higher wind speeds. More intense sunlight means more evaporation and stormier weather. Thus, a planet with more atmospheric pressure, but a slower rotation and less intense sunlight, would have fairly calm weather. Fast rotation with intense sunlight will make extreme weather events fairly common.
Another aspect of increased atmospheric density is that wind will have more force behind it. There is more air mass pushing against objects. Trees and plants would need to adapt to resist being uprooted by increased air pressure. In the movie, The Martian, you see the astronauts fighting against the high-speed Martian winds. In reality, there is so little atmosphere on Mars that even at such high speeds there is barely any effect. That lack of atmosphere is what allows the winds to get up to such high speeds. There is a lack of atmospheric resistance.
I mainly focused on explaining the effects of increased pressure, but you can apply the opposite effects on planets with decreased pressure. Planetary rotation and solar intensity effects would be the same, however.
BUT: the light absorption of gases increases with the pressure (e.g. greenhouse gases, like CO2, CH4, etc. but also water vapor absorbs), thus the air temperature increases. This way the water evaporates faster, which might increase relative humidity and this way also precipitation. (Note: it's probably not this simple, because air temperature also increases, making cloud formation harder?/less likely?/on a higher altitude?).
Higher atmospheric pressure is going to increase the amount of precipitation a planet would experience. Liquids would have less opportunity to gather in whatever cloud formations the planet gets. Lower air pressure would reduce the amount of precipitation the planet would get by increasing the opportunity for liquids to condense in clouds and just hang about in the air.