How long would it take for water vapor from an ocean asteroid impact to rain back down?

Earth is in dire need of water because of an already worsening climate change disaster (think now + a hundred years of out of control capitalist greed). Especially the climate change disaster's effect on temperature, capitalist greed against inland aquifers and increasing salinity in coastal aquafers because of sea rise.

I appreciate that you are building a world with such problems in mind, both the physics/logistic one and the humanitarian one. However, I think bringing more water from space is not the solution. Allow me to do a frame challenge.

Your comet will have 9.2 × 10¹⁸ kg. That's about 1% of the mass of the ice on the South Pole. You would elevate the oceans by the same amount we would if we just melted 1% of the Antarctic at once.

Consider that the total mass of the oceans is around The Earth's oceans have about 1.4 × 10²¹ kg, which is three orders of magnitude more than the comet. Your comet will flood coastal aquifers even more while causing no perceptible decrease in salinity. You'll just be putting mangroves underwater, where they will rot and release greenhouse gases.

Proper management of the water we already have here is the path to saving ecosystems. Merely shoving more water into it just makes things worse.

Kinetic Energy = (1/2)MV²

Where:

M is the mass of the asteroid just before it strikes the earth V is the velocity of the asteroid just before it strikes the earth

For example, consider an asteroid that is one kilometre in diameter and weighs 1.4 billion tonnes (M = 1.4×10^12 kilograms), and is traveling at 20 kilometres per second (V = 20,000 m/s). The kinetic energy would be equal to (1/2)×1.4×10^12×(20,000)² = 2.8×10^20 Joules.

14 hit earth (1 in land 13 in sea)

so it 13 x 2.8×10^20 = 3.64 x 10^21 Joules or 3.64 x 10^19 KiloJoules

ΔQ=cmΔt specific heat capacity of water(which equals 4.18710^3 J/(kg℃)) Average sea temperature is 30°C It is given by the equation Q=mL

Q= energy input m=mass of the matter to vaporize L=the specific latent heat

According to Wikipedia the value of the latent heat of vaporization of water is: L=2264.705 kj/kg

3.64 x 10^19 = (2264.705 x M) + (M x 4187 x (100-30))

3.64 x 10^19 = (2,264.705 x M) + (M x 4,187 x (100-30)) 3.64 x 10^19 = 295,354.705 M

M = 123,241,646,006,621 Kilogram of water

M = 123 Gigatons of water will be convert up into the atmosphere

1 mile² thunderstorm cloud = 72,000 tons

15 mile² thunderstorm cloud = 1,080,000 tons

15 mile² thunderstorm cloud last 30 mins

so our 123 Gigatons will continue to form into 123 millions of 15 mile² thunderstorm cloud above initial impact point and spreading around which take 30 mins to empty their bucket back down to earth

(123,000,000 x 30 )/( 60 x 24 x 365 ) =7020 years

but that is single one at a time which is not how reality work ,the thunderstorm would formed and spread faster

earth surface area is 510,100,000 km² or 196,950,711 mile²

13 million of 15 mile² thunderstorm cloud can fit in that

so.. if the asteroid hit and spread evenly (13 of 1 km diameter asteroid hit around the earth)

it will be downpour for (123 x 10^6 / 13 x 10^6) x 30 mins

5 hours..

but if compact into certain area say your capitalism corp pull it down to sea nearby USA (easy for them to go catch those rain by predicted that the wind will bring those thunderstorm cloud into land)and the said 13 asteroids spreading impact zone about the same size as USA outside the shore (with 1 miscalculated landing on New york instead)

9.834 million km² or 3.8 million mile²

200,000 of 15 mile² thunderstorm cloud can fit in that

it will be 123,000,000 / 200,000 x 30 mins so vaguely about 13-20 days

so if you want a good period of time for your story conflict like "capitalism corp covering up their mess" need about 3-4 month or so then just triple asteroid mass (or the impact zone must be more compact / or throw in more meteor or increased it mass)

but if you want something like a year of raining oh well you'll need quite bigger asteroids to do the job

(btw the dust from only 1 asteroid hitting land would dispersed faster giving it'll be raining a lot so those dust probably last around 30% of the time period)

Source

15 mile² thunderstorm cloud > https://wxguys.ssec.wisc.edu/2011/09/12/how-much-condensed-liquid-water-is-in-a-cubic-mile-of-fog/

asteroid energy > https://www.real-world-physics-problems.com/asteroid-impact.html

Sea temperature > https://www.seatemperature.org/

calculate water to stream > https://socratic.org/questions/calculate-the-amount-of-heat-required-to-convert-45-0-g-of-water-at-43-0-c-to-st#:~:text=Explanation%3A,the%20water%20to%20100%20degrees.&text=c%3D4187%20Joules%20per%20kilogram,specific%20heat%20capacity%20of%20water.

how long thunder storm last >https://www.google.com/search?newwindow=1&rlz=1C1OKWM_enTH866TH867&hl=en&biw=899&bih=923&sxsrf=ALeKk00Q2Jx2nBOHGsRrabrk60l9YppPQA%3A1594779746751&ei=YmgOX8C0LYfn9QOrq5KgAQ&q=how+long+thunderstorm+last&oq=how+long+thunderstr&gs_lcp=CgZwc3ktYWIQAxgAMgYIABAWEB4yBggAEBYQHjIICAAQFhAKEB4yBggAEBYQHjIGCAAQFhAeMggIABAWEAoQHjIICAAQFhAKEB4yBggAEBYQHjoECCMQJzoFCAAQkQI6BAgAEEM6CAgAELEDEIMBOgsILhCxAxDHARCjAjoCCC46BQguEJECOgUILhCxAzoCCABQi-0CWNmWA2CZnQNoAnAAeACAAXCIAdIMkgEEMjAuMZgBAKABAaoBB2d3cy13aXo&sclient=psy-ab