# Why is q used for specific humidity?

$q$ is the symbol used for specific humidity in many textbooks and papers (at least in meteorology and climatology, I'm not familiar with it in other disciplines). Where does this symbol come from, and what does it stand for?

• captial Q is used as specific heat in thermodynamics, perhaps they are related ?
– Neo
Commented Sep 5, 2014 at 16:16
• q (and r and w) refer in general to mixing ratios, not just with water vapor. Commented Sep 5, 2014 at 17:29

The specific humidity q is a quotient - mass of water vapor in mass of moist air. The mass is expressed per volume, i.e. the density of water vapor $\rho_v$ and the density of dry air $\rho_d$ are used for the definition of the quotient $q$ known as specific humidity:

$$q = \dfrac{\rho_v}{\rho_v+\rho_d}$$

• Although this is likely to be correct in my opinion, it would be nice if you could find a historical reference stating this. Commented Sep 7, 2014 at 0:59
• I don't know any reference for this explanation. Any help would be appreciated.
– BHF
Commented Sep 7, 2014 at 5:35
• I too was thinking that this might be the answer when I posted, but wasn't sure. Makes sense, since it's probably the most important mixing ratio in hydrology. +1 and I'll wait for a reference to accept :) Commented Sep 8, 2014 at 0:53

I haven't been able to find any particular references which hold themselves out as the origin of $q$ as the symbol of choice for specific humidity, but the origin of the term "specific humidity" itself appears to have been in an 1884 article by Dr. W. von Bezold, translated into English and published in the Smithsonian Miscellaneous Collections (Vol. 51) in 1910, and is defined therein as a quantity:

the quantity of vapor contained in the unit mass of moist air which can be conveniently called the "specific humidity"

(p.327)

At that time, $q$ was not used, but instead von Bezold chose $y$ as the symbolic representation of specific humidity in his subsequent equations:

$y$ the specific humidity or the quantity of vapor in a unit mass of moist air expressed in the fractional parts of this unit.

(p.328)

The first appearance of $q$ as a symbol for specific humidity that I've found is in Chapter 5 of Physics of the Earth, Vol. 1 (p. 151), published in 1931. Here, the author uses $q$ to mean specific humidity as though it is common knowledge, using it in equations before even defining it for the reader:

This makes $q$ a readily determined and quite conservative characteristic of any unsaturated air mass.

Followed a few sentences later by:

The relative humidity $f$ together with the specific humidity $q$ and absolute humidity $\rho_{w}$ are the quantities commonly used as measures of the moisture content of the atmosphere.

(p.137)

This 1931 reference is likely not the earliest use of $q$ to mean specific humidity, but is the earliest I was able to uncover.

Thus, it would seem that the use of $q$ as a commonly accepted symbolic representation of specific humidity originated sometime between 1884 and 1931. It seems quite plausible that, given the use of the word "quantity" in defining the term originally (and in later references that I'm unable to add links for), the choice of $q$ as the symbol for specific humidity finds its source in this definition.

Additional reference: Temperature inversions in relation to frosts, McAdie, Alexander, Cambridge, 1915. (p.5) (Full text at Hathi Trust)