# Measuring Water Vapor: Relative Humidity and Dew Point Temperature A "Parcel of Air" is an iminaginary body of air about the size of a large balloon that is used to explain the behavior of air. We will describe what is meant by the relative humidity and dew point temperature of air in a parcel. The parcel concept is used because we often would like to know what will happen to air as it moves in the atmosphere, and air tends to move together in blobs about the size of parcels (not molecule by molecule). The parcel concept will be extemely important in describing cloud and thunderstorm formation. For one thing, we will want to keep track of the relative humidity in an air parcel as it moves up and down in the atmosphere.

### Relative Humidity

The relative humidity in an air parcel is defined as the ratio of the amount of water vapor actually in the air to the maximum amount of water vapor required for saturation at a particular temperature

 water vapor content Relative humidity ≡ RH = water vapor capacity

For example, air with a 50 percent relative humidity actually contains one-half the amount of water vapor required for saturation. Air with a 100 percent relative humidity is said to be saturated because it is filled to capacity with water vapor.

One way to compute relative humidity is to use the concept of vapor pressure that was discussed on the previous reading page. The vapor pressure is used to keep track of the amount of water vapor in the air, and the saturation vapor pressure is used to keep track of the capaity for water vapor or the maximum possible amount of water vapor. Thus, the fraction {water vapor content} / {water vapor capacity} would be RH = {vapor pressure} / {saturation vapor pressure} or RH = e/es using the symbols defined on the previous page for vapor pressure and saturation vapor pressure.

However, following meteorological convention, we will use something called Mixing Ratio to keep track of the amount of water vapor in the air (instead of vapor pressure) and something called Saturation Mixing Ratio to keep track of the capacity or maximum possible amount of water vapor in the air (instead of the saturation vapor pressure}.

Below is the definition of the mixing ratio, which will be represented by the symbol capital U. Please do not be concerned or scared by the definition. The mixing ratio is just another way to specify the amount of water vapor in the air. It is used in the same way as the vapor pressure.

 actual (measured) mass of water vapor (in parcel) in grams Mixing Ratio ≡ U = mass of dry (non water vapor) air (in parcel) in kilograms

Again, we will use the mixing ratio of keep track of the amount of water vapor in air parcels ... the greater the mixing ratio, the more water vapor that is in the air.

Below is the definition of the saturation mixing ratio. We will use the Saturation Mixing Ratio, which will be represented by the Symbol capital U with a subscript s (Us) to keep track of the maximum possible amount of water vapor that can be in the air.

 mass of water vapor required for saturation (in parcel) in grams Saturation Mixing Ratio ≡ Us = mass of dry (non water vapor) air (in parcel) in kilograms

The Relative Humidity (RH) is simply the mixing ratio divided by the saturation mixing ratio.

 actual (measured) water vapor content U Relative Humidity ≡ RH = = maximum possible water vapor amount (saturation) Us

You are expected to know this equation for relative humidity and to be able to use it to solve simple problems. Just as with saturation vapor pressure, the saturation mixing ratio, which specifies the maximum amount of water vapor that can be in the air, is determined by the air temperature ... the higher the air temperature, the greater the saturation mixing ratio. We will use pre-computed tables of saturation mixing ratio to help solve problems. You should open the tables and make sure you understand the relationship between air temperature and the saturation mixing ratio, which is, as the air temperature increases, the saturation mixing ratio increases rapidly (exponentially). When using these tables make sure to use the correct temperature table, Fahrenheit or Celsius.

Let's go through an example.

A. What is the RH of an air parcel with a temperature of 25°C and a water vapor mixing ratio of U = 8 g/kg?

• Step 1. Use table of saturation mixing ratio to get Us. Reading from the Celsius table, for T = 25°C, Us = 20.1 g/kg. This specifies the maximum amount of water vapor that can be in the air when the air temperature is 25°C.
• Step 2. Use the RH equation. RH = U/Us = 8/20.1 = 0.398 or 39.8%

B. Continuing the example. What will the RH of the air in the parcel be if the parcel is cooled to T = 15°C with no change in the water vapor content?

• Step 1. Use table of saturation mixing ratio to get Us. Reading from the Celsius table, for T = 15°C, Us = 10.6g/kg. Note that the maximum amount of water vapor that can be in the air is much lower now that the air temperature is lower.
• Step 2. Use the RH equation. RH = U/Us = 8/10.6 = 0.755 or 75.5%
We can see that RH by itself does not indicate the actual amount of water vapor in the air because it has a dependence on the air temperature. In the example above, even though the actual amount of water vapor in the air was the same in parts A and B, the relative humidity was different because Us changed due to the temperature change. In fact there are two ways RH can change: (1) Change the water vapor content of the air (changes the mixing ratio, U, which is the numerator of the RH equation) and (2) Change the temperature of the air (changes the saturation mixing ratio, Us, which is the denominator of the RH equation).

Most people use Relative humidity to describe the water vapor content of the air, but it is widely misunderstood. Relative humdity in itself does not indicate the actual amount of water vapor in the air because it depends on temperature. For example, an air parcel at a temperature of 10°C with RH = 100% contains less water vapor than an air parcel at a temperature of 25°C with RH = 50%. You should be able to convince yourself of this by using the relative humidity equation and the table of saturation mixing ratios.

### Dew Point Temperature

The dew point temperature (Td) is defined as the temperature to which an air parcel would have to be cooled (with no change in its water vapor content) in order for it to be saturated with water vapor. It is determined by the amount of water vapor in the parcel, i.e., as the mixing ratio, U, increases, the dew point temperature, Td increases. If you know the actual mixing ratio in an air parcel, you can use the table of saturation mixing ratios to get the dew point temperature.

The dew point temperature is the answer to this question: "Given the amount of water vapor that is in a parcel, what would the air temperature have to be for the parcel to be saturated with that amount of water vapor?" The dew point temperature does indicate the actual vapor content of the air: the higher the dew point, the more water vapor in the air. You should realize that the dew point temperature is not something that is measured with a thermometer. It is really used to indicate the amount of water vapor that is in the air.

You are expected to be able to use the Relative Humidity equation and the table of saturation mixing ratios to perform simple calculations of dew point temperature. So far we have used the saturation mixing ratio tables to correspond air temperature in the left hand column with the saturation mixing ratio in the right hand column. The saturation mixing ratio tables are also be used to correspond the dew point temperature, Td in the left hand column with the mixing ratio, U, in the right hand column. In other words the actual amount of water vapor in the air can be specified using the mixing ratio or the dew point temperature.

Dew point temperature calculation example.

If the air temperature is T = 10°C and the relative humidity is RH = 50%, what is the dew point temperature, Td?

• Step 1. Use table of saturation mixing ratio to get Us. Reading from the Celsius table, for T = 10°C, Us = 7.6 g/kg.
• Step 2. Use the RH equation. In this example we know the relative humidity and the saturation mixing ratio and we will use the RH equation to first calculate the mixing ratio. Simply rearranging the RH equation, U = (RH) x (Us) = (0.5) x (7.6 g/kg) = 3.8 g/kg.
• Step 3. Use the table of saturation mixing ratios to find the dew point temperature. Locate U = 3.8 g/kg in the right hand column. The corresponding entry in the left hand column is the dew point temperature, Td = 0°C

The difference between air temperature and dew point temperature can indicate whether the relative humidity is low or high.

• when the air and the dew point temperatures are far apart, the relative humidity is low
• when the air and the dew point temperatures are close to the same value, the relative humidity is high
• when the air and the dew point temperatures are the same, the air is saturated and the relative humidity is 100 percent.

As mentioned, the dew point temperature is a measure of the amount of water vapor that is in the air. So if you wanted to compare the amount of water vapor in the air at two different locations, the one with the higher dew point temperature has the greater water vapor content. A graph of the dew point temperature with time indicates how the amount of water vapor in the air changes at a fixed location. Often there is an increase in dew point temperature just before and after a rain event.

A couple of links to dew point information:

dew point temperature and relative humidity on the Univ. of Arizona campus over the last 24 hours. Click on the weekly or monthly plots at the bottom of the page to see a longer time series of changes in dew point temperature. Look at how the dew point temperature and relative humidity change on days when precipitation was measured on campus.

U.S. map of current dew-point temperature. The locations on the map with the higher dew point temperatures have more water vapor in the air. However, the map does not indicate much about the relative humidity around the United States. Why not? What other information would you need to be able to determine values of relative humidity?

### Dew and Frost

Normally, near the Earth's surface, the relative humidity is less than 100%, therefore, net evaporation is occurring since the rate of evaporation is faster than the rate of condensation. To convince yourself of this, leave out an uncovered glass of water. The water will eventually evaporate. In fact the lower the relative humidity, the faster the rate of net evaporation. Once evaporated from the surface, water vapor moves around with the rest of the air.

Occasionally, there may be net condensation occurring near the Earth's surface. If air near the ground is cooled below its original dew point temerature, fog will result. Fog is nothing more than a cloud at ground level. We will talk more about clouds soon. Beside fog, are there ever situations near the Earth's surface when net condensation occurs? ANSWER: Yes, dew and frost. When the surface temperature of an object becomes colder than the dew point temperature of the surrounding air, water vapor from the air will condense onto the surface of the object, since the rate of evaporation is slower than the rate of condensation at the object's surface. This will be seen as condensed water on the surface of the object.

• Dew(liquid water drops) if the object is warmer than 0° Celsius
• Frost (ice) if the object is colder than 0° C. NOTE: frost forms by the process of deposition (water vapor --> ice). It is not frozen dew.
The dew point temperature can be defined as the temperature to which an object must be cooled in order for condensation (dew or frost) to form on the object. Natural dew and frost are most common during the late night and early morning hours. After the sun sets below the horizon, the surfaces of solid objects generally cool more rapidly than the overlying air. If the surface cools below the dew point temperature, then dew or frost will condense onto the surface. An everyday example of dew formation is the condensation that happens on the outside of a cold can of soda or a glass of ice water. The liquid water drops that form on the outside of the can came from the air as water vapor condensed into liquid. It tells you that the can must be colder than the dew point temperature of the air. Here in the desert, during times when the dew point temperature is low (often well below 0° C), condensation does not form on the sides of a cold can of soda, since the surface temperature of the can is not colder than the dew point temperature of the air. But in a more humid climate where the dew point is higher, you will see this type of condensation more often. Dew on grass Frost on grass

### Summary for how Water Behaves Based on Relative Humidity

You should understand the points made below. You can apply these points to explain what will happen under conditions where the relative humidity is known.

• If RH = 100% (Td = T), there will be no net evaporation or condensation, since the rate of evaporation is equal to the rate of condensation.
• If RH < 100% (Td < T), any liquid water present will evaporate with time, since the rate of evaporation is greater than the rate of condensation. This is the typical situation at the Earth's surface.
• If RH > 100% (Td > T), water vapor will condense to liquid water, since the rate of condensation is greater than the rate of evaporation. This is the condition for dew and frost formation. It happens when the surface temperature of an object is colder than the dew point temperature of the surrounding air. Net condensation will continue as long as the RH is greater than 100%. Net condensation removes water vapor from the air, which reduces the water vapor content in the air. Without a continuing source of new water vapor, this will cause the dew point temperature and relative humidity to lower with time. If the RH drops down to 100%, then the rates of evaporation and condensation are equal and net condensation (dew formation) ends.

### Example Calculations

ATMO 336 students are expected to be able to perform two types of calculations. Examples of each type are shown below.

#### Type 1. Given the air temperature and the dew point temperature, determine the relative humidity

If the air temperature is 35°C and the dew point temperature is 20°C, determine the relative humidity.

• Step 1. Use the saturation mixing ratio table to look up the saturation mixing ratio, Us, based on the air temperature, T. Make sure to use the Saturation Mixing Ratio Table for air temperature in Celsius. The table will always be provided for you. Simply find the air temperature in the left hand column and the corresponding entry in the right hand column is the saturation mixing ratio as shown here.
For T = 35°C, US = 36.6 g/kg.
• Step 2. Use the same table of saturation mixing ratios to look up the mixing ratio, U, based on the dew point temperature, Td. Simply find the dew point temperature in the left hand column and the corresponding entry in the right hand column is the mixing ratio as shown here.
For Td = 20°C, U = 14.7 g/kg.
• Step 3. Use the relative humidity equation to compute the relative humidity, RH, by plugging in the values for mixing ratio, U, and saturation mixing ratio, US
RH = U / US = 14.7 / 36.6 = 0.40
Relative humidity is typically expressed as a percentage out of 100, thus RH = 40%.

#### Type 2. Given the air temperature and the relative humidity, determine the dew point temperature

If the air temperature is 30°C and the relative humidity is 33%, determine the dew point temperature.

• Step 1. Use the saturation mixing ratio table to look up the saturation mixing ratio, Us, based on the air temperature, T. Make sure to use the Saturation Mixing Ratio Table for air temperature in Celsius. The table will always be provided for you. Simply find the air temperature in the left hand column and the corresponding entry in the right hand column is the saturation mixing ratio.
For T = 30°C, US = 27.2 g/kg.
• Step 2. Use the relative humidity equation to compute the mixing ratio, U, by plugging in the values for the saturation mixing ratio, US and the relative humidity, RH. Note that the Relative humidity is given as a percentage. This must be converted to a decimal number to use in the equation. In this example, the decimal equivalent for 33% is 0.33.
U = (RH) * US = 0.33 * 27.2 g/kg = 8.98 g/kg.
• Step 3. Use the Saturation Mixing Ratio Table for air temperature in Celsius to look up the dew point temperature, Td based on the mixing ratio, U. Simply find the mixing ratio in the right hand column of the table and the corresponding entry in the left hand column is the dew point temperature as shown here. Note that the value may fall in between two rows of the table as in this example. When that happens, make your best estimate for the dew point temperature by interpolating between the nearest values in the table.
In this example, the dew point temperature is about 12°C