# Convert specific humidity to relative humidity but without having all variables available?

I was wondering if there is a way to obtain relative humidity from specific. My constraint is that I am not trying to solve a problem by hand. I am downloading data for a specific region, in order to construct a multi model for climate modelling. Unfortunately, I do not have access to any dataset that I want. The following variables have available datasets which I can use:

-specific humidity (Dimensionless, Amount of moisture in the air divided by amount of air plus moisture at that location.)

-maximum and minimum air temperature

-mean daily wind speed at 10m

-vapour pressure (hPa)

-sum of precipitation (mm/day)

-potential evapotranspiration from a crop canopy (mm/day)

Is there any equation that I can use to obtain relative humidity?

• It should be possible to calculate the relative humidity at any given time if you know the specific humidity, the atmospheric pressure, and the vapour pressure at that time. Do you have the atmospheric pressure? Also, how you go about it will depend on how the specific humidity is defined. Is "amount of moisture" and "amount of air plus moisture" measured by number of moles, or by mass? Aug 6 at 17:31
• Hey @MichaelSeifert . To be honest, I am not familiar with the physics part of what is needed. I am doing my thesis, which is data science related and I am downloading data regarding a specific region. Basically I am downloading datasets of the variables I mentioned and creating a multi model with them and then some calculations to minimize bias, statistical errors etc. My phd promotor asked me if we can somehow calculate relative humidity, based on the datasets that I have mentioned in my post because these are only the data we can have access to
– Alex
Aug 6 at 17:39
• Is the "vapour pressure" you have the equilibrium vapour pressure (which is what the phrase usually refers to)? Or is it actually the "partial pressure of water vapour"? If it's the latter, then you have a shot at it. If it's the former, you will need more data to get relative humidity. You might want to take a close look at the metadata on the data set and see if it clarifies this issue. Aug 6 at 18:06
• @MichaelSeifert thank you very much for the reply! I will contact the site to ask them because they do not specify it. If it is the latter, what is the method to obtain relative humidity?
– Alex
Aug 7 at 10:42
• See my answer below. Aug 7 at 17:49

"Vapour pressure" usually means the equilibrium vapour pressure of water, which is the partial pressure of water vapour in air when the air "holds" its maximum amount of water. In other words, if the partial pressure of water vapour is equal to the equilibrium vapour pressure, then you are at 100% relative humidity. Note that equilibrium vapour pressure varies rather strongly with temperature.

In a more general case, the relative humidity of an air sample is defined as the ratio of the partial pressure of water vapour in the sample to the equilibrium vapour pressure of water at that temperature: $$\text{relative humidity} = \frac{\text{partial pressure of H}_2\text{O}}{\text{equilibrium vapour pressure}}$$ So if you could figure out the partial pressure of the water vapour, you could then infer the relative humidity.

If you knew the overall atmospheric pressure at a given time, and you knew the fraction of the air (either by mass or by moles) that was water vapour, you could use Dalton's Law to figure out the partial pressure of the water vapour, and thereby infer the relative humidity. But if you just know the equilibrium vapour pressure of water and the specific humidity, without knowing the total atmospheric pressure, there's no way to get the relative humidity; a given specific humidity can correspond to different partial pressures of water vapour, depending on the overall atmospheric pressure.

That said, it is conceivable that the data set is providing the partial pressure of water vapor as "vapor pressure". If this is the case, then you know the numerator of the equation above and you would need to figure out the denominator. Thankfully, the equilibrium vapour pressure of water is a well-studied quantity. It does vary strongly with temperature; but so long as you have the temperature at which the measurement was made, then it is straightforward to figure out the equilibrium vapour pressure (either via a lookup table & interpolation, or via one of the approximate formulas linked in the above article) and then to find the relative humidity.

• Hello again! I was wondering if it is possible to calculate humidity from pressure and temperature
– Alex
Aug 9 at 20:15
• @Alex: Which pressure? Total atmospheric pressure, the equilibrium vapour pressure, or the partial pressure of water? The answers are "no", "no", and "yes but it's not straightforward" respectively; the latter two are explained in my answer above. Aug 9 at 20:34