There actually was an IRL example of doing what you suggest. I wrote about it in this piece.
Understanding WWIII, what’s in it for China?
The 1883 eruption of Krakatoa caused a volcanic winter.
In the year following the eruption, average Northern Hemisphere summer temperatures fell by 0.4 °C (0.72 °F).
The record rainfall that hit Southern California during the water year. Has been attributed to the Krakatoa eruption.
From July 1883 to June 1884 Los Angeles received 38.18in and San Diego 25.97in of rainfall.
Normal rainfall for LA is 14.77in per year.
Because, when you suddenly cool the atmosphere down. Water falls out of it. Cool air holds less water than warm air.
The eruption injected a huge amount of sulfur dioxide (SO2) gas high into the stratosphere. This was transported by high-level winds all over the planet.
This led to a global increase in sulfuric acid (H2SO4) concentrations in high-level clouds. The resulting increase in cloud reflectivity (or albedo) reflected more incoming light from the sun away from the Earth.
Which cooled the entire planet until the sulfur fell to the ground as acid rain. A process that takes 3–5 years.
So we know exactly how to Geoengineer the Climate.
THE RAINFALL WOULD BE BIBLICAL.
