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specific humidity to relative humidity given temperature and elevation

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  • specific humidity to relative humidity given temperature and elevation


    I am having trouble finding a formula to convert specific humidity to relative humidity. I believe it is a simple task, but I am just not getting it.

    I am given the air temperature, the specific humidity and the elevation. Could someone help me out? Thank you.

  • #2
    To calculate relative humidity from specific humidity, first, if you are using Fahrenheit, convert the air temperature and dew point temperature to Celsius.
    Subtract 32 from the Fahrenheit temperature, then divide the result by 5/9.

    ( F - 32 ) 5 / 9 = C*

    Then you need to find the saturated vapor pressure for your temperature
    SP = 6.11 * 10 ( ( 7.5 * Cs ) / ( 237 + Cs ) )

    Do the same thing with your dew point.
    DP = 6.11 * 10 ( ( 7.5 * Cd ) / ( 237 + Cd ) )

    When you have these done, relative humidity is
    RH = SP / DP * 100

    If you don't have a dew point I'm afraid you're stuffed. Elevation is a red herring in this process, since dew point is calculated by determining how dry the air is.


    • #3
      There is a thread called "The Humidity Resource" in our Resource forum. Unfortunately, it is so old that it is archived and you have to use the search function to find it, or the link:

      Your request is non-trivial as you have probably the least useful specification of humidity to work back to relative humidity. What you actually need is the actual water vapor pressure.

      The specific humidity, SH, is the ration of mass of water vapor to mass of dry air. Step one is mixing ratio, MR, in which the denominator is mass of moist air, MR = SH/(1-SH).

      Then you need station pressure, the actual local atmospheric pressure, p, not corrected to sea level. (If you don't have a barometer that reads this, see deep in the thread for a way to use altimeter equation and altimeter setting from your local airport. This value varies with weather patterns. You can "unsolve" the mixing ratio equation for absolute water vapor pressure, ea

      ea = p*MR/(0.622 - MR)

      Relative humidity is the ratio of actual to saturated water vapor pressure, ea/es. Saturated water vapor pressure as a function of temperature is a very complex equation, and it is usually approximated over moderate temperature spans by simpler equations. For most reasonable temperatures, the Bolton equation is recommended over -30C to 35C, other variations tweak the coefficients for 0 C to 50 C. If you have to cover a wide temperature range without switching equations, use the Sonntag equation, but it can only be reversed to solve for temperature by numerical means.

      Note that specific humidity varies with the barometer (elevation and weather patterns). Unless you particularly need or want this behavior, if you are looking at a spec, water vapor pressure or dew point (reported by local NWS station) is a more useful parameter. The dew point remains nearly constant until a new air mass moves in, while relative humidity varies throughout the day with temperature, as saturated water vapor pressure is a strong function of temperature.