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Saturation Mixing Ratio

Saturation mixing ratio (Ws ) is the theoretical maximum amount of water vapor that air at a specific temperature and pressure can hold. When air is saturated, it cannot hold any additional water vapor. To find this value at any pressure level, use the dashed green saturation mixing ratio lines on either side of your plotted temperature. Interpolate the value of your temperature plot using the scale on the mixing ratio lines printed just above the 1,000-millibar level. For instance, if your 500-millibar temperature is 15.6C, this falls halfway between the green dashed lines labeled 2.5 and 2.0, you would interpolate the value to be 2.25. Since these lines represent grams of water per kilogram of air, you know that a parcel of saturated air with a pressure of 500 millibars and a temperature of 15.6C can hold 2.25 grams of water vapor per kilogram of air.

Actual Mixing Ratio

To find the actual mixing ratio (W), often called simply the mixing ratio, interpolate the value of the same dashed green lines at the plotted dew point temperature for temperatures above freezing and down to -12C. For levels where the air temperature is below freezing, evaluate the value of the mixing ratio line through your calculated frost point temperature. You will have two sets of values in the 0C to -12C range. For levels where the air temperature is below -12C, you need only evaluate the mixing ratio through the frost point temperature. When we do this, we find how much water vapor is held by a parcel of air at the specified pressure level. For example, if your 800-millibar temperature is 5.0C and your dew point temperature is 3.0C, you should read the value of your mixing ratio line through the dew point temperature as 6.0 grams of water per kilogram of dry air (or simply 6.0 g/kg). But lets look at a case where your temperature is between 0C and -12C. Say your 600-millibar temperature is 10.0C and the dew point temperature is 15.0C. You should first calculate a frost point temperature. In this case, it is 13.5C. Now evaluate the mixing ratio through both the dew point temperature and the frost point temperature. You should find a value of 2.0 g/kg for the dew point temperature and 2.25 g/kg for the frost point temperature. In the next section we will use this same example to highlight the difference between the two values of the actual mixing ratio.

Now that you know how to find the saturation mixing ratio and the actual mixing ratio, what do you do with them? Lets find out.

Relative Humidity

Relative humidity is a ratio, expressed in percent, of the amount of water vapor in the air (actual mixing ratio) compared to the amount of water vapor the air can hold (saturation mixing ratio). Since we have already found these values, we can find the relative humidity for any plotted pressure level by using the formula  

Since the units (grams per kilogram) cancel, we are left with a number, expressed as a percentage.

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