# What does the notation “kg kg-1” for units mean for specific humidity

I am using a data set from Justin Sheffield at Princeton that includes specific humidity. The description is as follows:

"Reanalysis 6-hourly specific humidity interpolated to 1.0deg with account for elevation changes and scaled to maintain consistency with reanalysis relative humidity and CRU TS3.0 monthly air temperature";
The units are = "kg kg-1"

What does this mean? Does it mean kg/kg so essentially dimensionless? Because I have seen around specific humidity measured also in g/kg, maybe that was wrong? These two pages give the same definition of specific and absolute humidity, I thought they were different things: http://www.nzifst.org.nz/unitoperations/drying3.htm http://tigge.ecmwf.int/tigge/d/show_object/table=parameters/name=specific_humidity/levtype=pl/

• Humidity is generally expressed as a ratio, which is dimensionless. E.g $kg/kg$ as in your example. – Tactopoda Jun 23 '15 at 8:32
• $1\,{\rm g}/{\rm kg} = 0.001$. Yes, that's technically a valid (dimensionless) unit. – Ilmari Karonen Jun 23 '15 at 10:13

Just to expand on yo's answer:

It's unit-less so, mathematically, you could omit the kg/kg. However then the reader wouldn't know if you're expressing a quantity as a percent weight or a percent volume which are different.

Yes, the unit is kilogram per kilogram, but it means kilogram of water (moisture) per kilogram of air.

The basic idea is that by mentioning $\mathrm{kg}\, \mathrm{kg}^{-1}$ you make it clear that you measure the weight. You can think of it as

$$0.01\, \mathrm{kg}\, \mathrm{kg}^{-1} = 1\, \mathrm{wt.}\%.$$

This is to avoid confusion with $\mathrm{vol.}\,\%$.

• kg is mass, N would be weight, right? – Thomas Weller Jun 23 '15 at 20:53