Water Vapour and Relative Humidity

An Eccentric Anomaly: Ed Davies's Blog

It's often said that 100% relative humidity (RH) corresponds to the amount of water vapour that the air can hold at the relevant temperature. I think some people have an image of the air being like a sponge and when all the little holes become full and the air becomes saturated the rest drips out. This is wrong and, in some cases, seriously misleading but just close enough to right in common cases that the myth keeps getting repeated. Part of the problem is that the easiest way to phrase discussions reinforces the idea.

Air doesn't hold water vapour. Water vapour, oxygen, nitrogen, argon, carbon dioxide and so on are all gasses which can coexist in the same volume with very little effect on each other.

Each gas operates independently as a reasonably close approximation to an ideal gas with its own density and pressure determined by the number of molecules present (usually counted in moles), its molecular mass and the temperature. Each gas's pressure is called its partial pressure and the sum of these for all the gasses present somewhere is the atmospheric pressure there. The partial pressure of water vapour is often just called the vapour pressure.

The amount of oxygen in the Earth's atmosphere has varied considerably over its lifetime but recently (for the last half billion years or so) it's stayed around approximately 20% (15 to 35%). If the oxygen content goes up to much more than that there are more fires which brings it down again. Conversely, if it drops much lower animals start dropping as well, breathing in less oxygen and eating less vegetation, resulting in the oxygen level rising again.

We don't say that this equilibrium is the result of the nitrogen being able to “hold” that amount of oxygen. Similarly, the amount of water vapour in the atmosphere is controlled by equilibrium processes and it is equally wrong to think about the air being able hold some quantity.

The equilibrium processes are, of course, evaporation and condensation of water vapour on various surfaces.

100% relative humidity for a given temperature corresponds to the vapour pressure at which evaporation and condensation on a flat surface of pure liquid water just balance. If the vapour pressure is lower there's less condensation but still the same amount of evaporation so the vapour pressure increases towards that for 100% RH. If the vapour pressure is higher there's more condensation and the pressure drops.

I prefer the term “equilibrium vapour pressure” rather than “saturated vapour pressure” because it reflects this process much better.

The rate of evaporation increases with the temperature and with reduced amounts of surface tension. Consequently, the equilibrium vapour pressure is very dependent on the temperature: as a very rough rule of thumb it doubles for every 10 °C increase in temperature.

The surface tension, in turn, depends on any materials dissolved in the liquid and the curvature of the surface.

My, perhaps simplistic, understanding of the effect of curvature of the surface is that water molecules in the liquid close to the inside of a convex surface have slightly fewer neighbouring liquid water molecules attracting them and therefore can evaporate more easily. Conversely, those in the liquid close to a concave surface have more neighbours and so can evaporate less easily.

This has a practical effect in building science. Liquid water condensing in a material with small pores, like wood or plaster, will tend to have a concave meniscus and so reduced evaporation. AIUI, this is why the water content of wood and the like tends to increase rapidly once the relative humidity passes 95% or so rather than, as you might expect if you think in terms of air holding water, at 100% RH.

Conversely, water droplets condensing in the air have a convex surface and therefore a greater rate of evaporation. Consequently the equilibrium vapour pressure is higher and relative humidities greater than 100% will be reached before droplets grow.

A complicating factor with droplets forming in air is that they need to form around condensation nuclei, particles of dust, salt or whatever. If the air is completely clean (as can be set up in laboratory experiments) the relative humidity can be very high before condensation occurs (300%, I've read somewhere).

In the more common case where there are lots of particles for condensation to form on, much lower RHs apply, something like 102 or 103%. When a droplet first starts to form it is, of course, very small and therefore has a tight radius of curvature. As it grows the curvature reduces and therefore the rate of evaporation also reduces meaning that once a droplet starts to grow it then does so quite rapidly. (There's also a complicating factor that the particle which formed the nucleus of the droplet will likely dissolve in the droplet and, as the droplet grows, become more dilute which also affects the evaporation.)

This effect of droplets growing rapidly once they reach a particular size (and evaporating rapidly once they shrink to a certain size as they come to drier air) is readily observable in everyday life: clouds in the sky have relatively sharp boundaries rather than being fuzzy objects which get gradually thinner with distance as you should expect if you believe the “holding water” theory of air. If you've ever climbed into a cloud in a glider then flown out of the side again you'll know that the transition is often (though not always) quite rapid - over a few 10s of metres. You see the same thing in an airliner but that's going quite a bit quicker so the speed of the change is a bit less remarkable.

I first came across this idea on the Bad Meteorology site, specifically the Bad Clouds page. There's a lot more detail, particularly on formation and evaporation of raindrops, in Robin McIlveen's book Fundamentals of Weather and Climate of which I'm pleased to have a copy of the second edition as it's now out of print, I believe. Sadly, some other meteorology textbooks cover this topic less well to the point of being quite misleading.

The phraseology about the amount of water air can hold at some temperature will persist because it's such a convenient shorthand. But it would really help if people didn't only use it and, at least once in any bit of writing referencing the idea, use a longer form of words which more closely reflects the actual processes involved.

Update: 2017-03-27: A few clarifications added following comments by Tom Foster.