Thanks Hyperion, I agree that it's interesting to look at the potential contribution of atmospheric water to Arctic sea ice melt so I will take you up on your 'peer review' offer...

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Quickstab at what this setup might mean numerically. Peer review and alternative approaches most welcome:

1,680,000,000,000,000J

18.748 kg/sqm

200km x 50kmph (ballpark flow estimate) x 24hr = 240 000 sqkm = 240 000 000 000 sqm

240 000 000 000 sqm x 19 kg x **4200J** = 19,152,000,000,000,000 Joules per day

=19.52 petajoules per day

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That's the specific heat capacity of water - the amount of energy required to raise the temperature of 1 kg liquid water by 1 degree Kelvin \ Celsius. Better to use the heat of evaporation as the "Total precipitable water" is almost all vapour (use "Total cloud water" option to see the small part that isn't) and can melt ice by condensing. This contribution to heating the ice is much larger than the heats from temperature changes.

Water properties here.It's actually even easier to use the ratio of heats of vaporisation to fusion.

Latent heat of melting - 334 kJ/kg

Latent heat of evaporation - 2257 kJ/kg

Ratio ~ 2257 / 334 ~ 6.76. So each kg of water vapour can, by condensing, cause the melt of nearly 7 kgs of ice.

Expressed in scientific notation, you estimated 2.4e11 m^2 of moist air entering the Arctic per day, carrying 18 kg/m^2 of water vapour, so on multiplying you say about 4e12 kg/day of water vapour entering the Arctic.

From above, this could melt 2.4e11 x 18 x 6.8 kg/day ~ 3e13 kg/day of ice.

To see if this would be a relevant amount, we should ask how many kg of ice are in the Arctic?

From PIOMAS, we see that the volume of Arctic sea ice at the end of the freeze season is around 20 000 km^3 ~ 2e13 m^3. Ice weighs around 900 kg/m^3, so this is ~ 2e16 kg of ice.

On comparing the two, it would take several hundred days to melt all the ice at the assumed rate of ingress of water vapour and assuming a large fraction of it condenses to melt ice.

As an initial impression, I would also say that the rate of ingress you assume is anyway much larger than would be typical, perhaps by an order of magnitude or more.

So this back-of-the-envelope calculation suggests that the ingress of atmospheric water vapour into the Arctic can't account for a large fraction of the yearly ice loss. However, it wouldn't be surprising if it contributed at the percent level or maybe up to a few percent of the ice loss.

Given the observed rise in atmospheric moisture beginning around the start of 2016, this could still mean a significant rise in sea ice loss by this mechanism.

Presumably this has been studied at a more rigorous level. Does anyone know of such a study and their findings?

EDIT: already answered and it has been studied. Thanks, Jai Mitchell.