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Cause of Sea Level Rises

According to the report in World Economic Forum, sea level rise is the result of two effects:

  • Ice melting.
  • Ocean water expanding because of the temperature increase.

They give the prediction of an unavoidable 1-2m sea level rise. I was wondering what the effect of an increase in humidity, because warm air can hold more water vapor, does have on the effect of sea levels rising.

Temperature Increase - Effect on Atmosphere

I only found information about the temperature increase of the earths surface (see for example National Centers for Environmental Information), which predicts a wide range of possible futures ranging from 2°C to 5°C. Is there information on how the increase of surface level temperatures affect atmospheric temperatures? Is there more exchange between the different layers of the atmosphere or is there a linear relation between the surface temperature and the troposphere and stratosphere temperatures?

Vapor Content of Air

Additionally, I know that the Clausius–Clapeyron Equation can be used to calculate evaporation pressures, but I'm unsure on how to apply the equation to the sub-question of how much water can air hold at a given temperature (and pressure). Can someone help me understand how the maximal humidity of air (or the mass of the water vapor in the air) can be calculated?

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    $\begingroup$ The search term is 'steam tables'. There are various parameterizations of dew point across temperature ranges as well. $\endgroup$
    – Jon Custer
    Commented Sep 9 at 14:35
  • $\begingroup$ See en.wikipedia.org/wiki/Dew_point for an overview. $\endgroup$
    – Jon Custer
    Commented Sep 9 at 15:11
  • $\begingroup$ Thank you for the tipps! I just found Psychrometric Charts to be a good resource for figuring out the water content of air. But I still have a hard time estimating the average relative humidity - typically air holds less water than at the dew point I assume. For a relative humidity of 50%, air at the average surface temperature of 15°C can hold 5x its weight in water. at 100% its around 10 times. $\endgroup$
    – Znerual
    Commented Sep 9 at 15:28
  • $\begingroup$ At 15C the saturation water vapor pressure is about 1700 Pascal, and 1 atmosphere is 101325 Pascal, or water vapor is about 1.7% of the atmosphere. I don't see where you get '5x its weight in water' - that is not even close. $\endgroup$
    – Jon Custer
    Commented Sep 9 at 15:38
  • $\begingroup$ I played around with the flycarpet.net/en/psyonline Psychrometric Chart and it shows that for an ambient pressure of ~10^5 Pascal and 1700 Pa of saturation water pressure (at the given 15°C for a 50% relative humidity) the humid ratio is 5.38. Is there a misunderstanding on my side on what the humid ratio means? $\endgroup$
    – Znerual
    Commented Sep 9 at 15:44

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First it is good to understand how much more mass the ocean has than the atmosphere.

Atmospheric pressure is $14.7$ lb/sq inch or $1$ bar. This means the weight of a $1$ x $1$ inch column of air from sea level to space is $14.7$ lb. Air covers $100$ % of the earth.

Oceans cover $70$ % of the surface to an average depth of $12000$ feet. A $1$ x $1$ inch column of water that weighs $14.7$ lb is $32$ feet tall. This means the pressure in the ocean goes up $1$ bar for every $32$ feet of depth. At $12000$ feet, the pressure is $375$ bar. If the ocean covered the whole Earth to this depth, it would weigh $375$ times the atmosphere's weight. $70$ % of this is $263$ times the atmosphere's weight.

The atmosphere can soak up water until it is saturated. We call this $100$ % humidity. The amount of water air can hold depends on temperature. $99$ % of the water vapor in the atmosphere is in the troposphere, the lowest layer $4$ to $12$ miles thick. And half is in the bottom $250$ meters.

The average temperature of the atmosphere is $17$ C at the surface.

The vapor pressure of water at saturation and $15$ C is $0.017$ bar. This means the weight of the water in the air is $1.7$ % of the weight of the air. It drops quickly to $0$ % at lower temperatures.

The average humidity is less. In moderate to humid tropical regions, $1$ kg of air might hold $12$ to $16$ grams of water. If we include polar regions, $1$ % might be a reasonable estimate for the average.

The density of air at the surface is $1.22$ kg/m$^3$. The volume of $1$ inch x $1$ inch x $250$ meters is $0.16$ m$^3$. It holds $0.195$ kg of air, or $2$ grams of water. This has a volume of $2$ cubic centimeters, or $0.06$ cubic inches. This is the typical water content of the bottom $250$ meters of the atmosphere. The rest of the atmosphere also has this much. The total water in a $1$ inch x $1$ inch column to the top of the atmosphere would condense to a layer $0.12$ inches tall.

Note that storms often drop more than this. Storms have clouds because the water content is higher than saturation. The water condenses.

This won't change things much. In a typical spot, it spends < $1$ % of the time raining or snowing.

Storms blow water from one spot to another. It isn't like all that water is in the atmosphere all the time, waiting to come down. Water evaporates from the ocean and rains on land. Then it flows back to the ocean.

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