And also warmer oceans evaporate more.
But... if warm air holds more moisture, sure, there's more moisture in the air. But there's no greater tendency for it to condense out in the form of rain, because warm air holds more moisture.
Can someone ELI5 why warmer air should lead to more rain, not just to more water vapor in the air?
Prior disclaimer: IANAC and IANAM
It can lead to either, depending on the local climate and circumstances. For an oversimplified explanation, compare the flooding in Pakistan and the drought in Europe:
- In Europe, abnormally high temperatures have increased the evaporation of top level water, because a greater proportion of water can evaporate into the atmosphere. As a result, even when it does rain, the water is more likely to evaporate again rather than soak into the soil and feed into the local drainage basin and eventually its river.
- In Pakistan, abnormally high temperatures have increased the water-holding capacity of the atmosphere. As a result, when the factors that normally trigger monsoon rains come into play, the amount of water that is released is disproportionately larger than the normal average.
If you have more water around, this process is stronger (as you have more available water to condense and energise the storm), eventually producing more rain.
This is the reason why you see the biggest thunderstorms in the tropics, where it is warm and moist.