10/4/99
HUMIDITY
Humidity is a measure of how much water vapor is in the air. There are a variety of ways to measure humidity. Some are proportional to the actual number of water vapor molecules in the air - these are measures of absolute humidity (e.g. vapor pressure, mixing ratio, dew point temperature). Other ways describe how close the air is to saturation (e.g. relative humidity ).
Evaporation, Condensation, and Saturation
To illustrate the concepts of evaporation, condensation, and saturation, Chapter 5 of Danielson begins with a thought experiment: Imagine an aquarium tank partially filled with water. There is a divider separating the liquid water below from empty space (i.e. a vacuum, no air molecules present) above. The tank, the air, and the water are all kept at a constant temperature. If you remove the divider, what will happen?
If you could view individual liquid water molecules on the water's surface, you would see that each molecule is loosely bound to its neighbors. Each of these molecules "wiggles" with a certain speed; the energy associated with this motion is called kinetic energy. Remember that temperature is really just a measure of the average speed at which these molecules are moving (i.e. a measure of their average kinetic energy). We use the term "average" because some molecules are moving faster, and some are moving slower. If the motion of a molecule - its kinetic energy - is great enough, the molecule can break its bonds to its neighbors and fly off into the space above the liquid. This is evaporation. Remember that the latent heat of vaporization for water is 600 calories per gram. This means it costs 600 calories of energy for 1 gram of water to evaporate. The higher the water's temperature, the more energetic (on average) the water molecules will be, and a higher fraction of them will be energetic enough to evaporate. (Since we keep everything at a constant temperature, there is always a ready supply of energy for evaporation.)
As more and more water molecules evaporate, we can measure the pressure these vapor molecules exert on the walls of the container - this is the vapor pressure, and it is commnonly expressed in millibars. It is an absolute measure of humidity: the more water vapor molecules there are at a given temperature, the higher the vapor pressure.
After some time, slower moving vapor molecules making contact with the liquid surface can become bonded with the liquid molecules again - this is condensation. Eventually, the rate of condensation will equal the rate of evaporation. When this occurs, the system is in equilibrium, since the number of vapor molecules in the region above the liquid water won't change - for every molecule evaporating, one is also condensing. This is saturation. The number of water vapor molecules in the region above the liquid is expressed as the saturation vapor pressure.
Imagine you repeated this experiment 100 times, each time changing the temperature of the system by one degree. You start at -50 degrees Celsius and ended at 50 degrees Celsuis. Each time the system reached saturation, you would measure the vapor pressure (how would you know saturation was reached?). If you plotted the value of the saturation mixing ratio for each temperature, you would obtain the graph in Figure 5.7, which shows that the saturation mixing ratio INCREASES with temperature. Why does the saturation mixing ratio increase with temperature? Because higher temperatures mean there is more energy available from the environment to go into evaporating water molecules (Another way to say this is "warm air holds more water vapor" - but we know this isn't exactly right. Air doesn't hold water molecules; it's the temperature that determines how much water evaporates before equilibrium is reached).
10/6/99
MEASURES OF WATER VAPOR IN THE ATMOSPHERE
- vapor pressure - the pressure exerted by water vapor molecules in the region above the liquid water surface, as in Figure 5.1. More generally, it is the portion of the total atmospheric pressure (approximately 1000 millibars at sea level) contributed by water vapor molecules. At room temperatures, Figure 5.3 shows that the vapor pressure at saturation is between 20-30 millibars - this is an upper limit to the vapor pressure at such temperatures (can you see why?).
- mixing ratio - another way to express the number of water vapor molecules in the air is the mixing ratio, which for our purposes is defined to be the mass (in grams) of water vapor contained in 1 kilogram of dry air (note the water vapor amount is measured in grams, while the dry air is measured in kilograms = 1000 grams.) Figure 5.7 show values of the mixing ratio at saturation for a range of temperatures. From Figure 5.3 and Figure 5.7 you can see that the amount of water vapor in the air at saturation increases with increasing temperature, whether we use vapor pressure or mixing ratio as the measure of humidity.
- dew point temperature - recall from earlier in Chapter 1 of Danielson that the dew point temperature is the temperature at which air becomes saturated. Put another way, when the air temperature and dew point temperature are equal, the amount of water vapor in the air is equal to the saturation vapor pressure for that temperature (Figure 5.3) and equal to the saturation mixing ratio for that temperature (Figure 5.7). If you know the air's dew point temperature, you can use these figures to determine how much water vapor is actually in the air. A higher dewpoint temperature will give you a higher value of vapor pressure and mixing ratio.
- relative humidity - back in Chapter 1, we said that the value of relative humidity was an indicator of how close the atmopshere is to saturation. Mathematically, the relative humidity is defined as :
mixing ratio r divided by the saturation mixing ratio r_s X 100%
If RH = 100 %, the mixing ratio is equal to its saturation value, and the atmosphere is saturated (i.e. rate of evaporation = rate of condensation). When the RH is 100 %, you also know that the air temperature and the dew point temperature are equal. In general, however, the air temperature and the dew point temperature are not equal, thus RH < 100 %, and the atmosphere is not saturated. How then, do clouds and fog and precipitation form? [The answer has to do with the fact that RH is relative to temperature; if you change the airs temperature (e.g. cool it down) and keep the mixing ratio the same, RH will increase.]
In practice, quantities like vapor pressure or mixing ratio are hard to measure. [Can you imagine how you might be able to take a sample of air and measure the pressure of just the water vapor molecules alone? Or how you might determine the mass of those water vapor molecules out of the millions of molecules making up your air sample?] However, the dew point temperature and the relative humidity are comparitively easy to observe.
The simplest way to determine the dew point temperature is to put a thermometer in a pitcher of room temperature water and then add ice to cool the water (this also cools the sides of the pitcher that are in contact with the air). Keep adding ice and monitoring the temperature until condensation forms on the sides of the pitcher. When this occurs, you have succeeded in cooling down the pitcher to the air's dew point temperature, so air in contact with the pitcher becomes saturated, and water vapor condenses to liquid water.[Here in the desert, dew point temperatures are often at or below freezing, so it might be necessary to dissolve table salt into the ice water. This will cool the ice water down a few more degrees below 32 F].
Relative humidity can be measured in a number of ways. One is by using the fact that human or animal hair actually changes length as RH changes (it increases in length as RH increases). This is the scientific basis for those bad hair days during monsoon season. A device for measuring RH using changes in hair length is called a hair hygrometer. Another method of measuring RH is using a sling psychrometer. This was demonstrated in class. See Chapter 5 in Danielson for a detailed description of how this instrument works.
10/8/99
Relative Humidity, Human Comfort, and Cloud Formation
Relative humidity depends on temperature
There are two ways that the relative humidity (RH) can change. First, you can put more water vapor in the air. This is equivalent to increasing the air's water vapor mixing ratio (r). Second, you can keep the amount of water vapor in the air constant and change the temperature of the air. Changing the air's temperature changes the saturation mixing ratio (r_s). As Figure 5.7 shows, as temperature goes up, so does r_s. Therefore, from the equation for calculating relative humidity above, as temperature goes up, the relative humidity goes down.
The relationship between RH and temperature is shown in Figure 5.14. As temperature increases throughout the day, while the dewpoint temperature (or equivalently, the actual mixing ratio) remains constant, RH goes down. RH is typically highest in early morning when temperatures are lowest. RH is lowest typically in afternoon, when temperatures are highest.
Heat Index
Relative humidity is important for your body's ability to cool itself through evaporation. Remember that evaporation of liquid water costs energy - about 600 calories per gram of liquid water - and that energy comes from the surrounding environment (i.e. latent heat). When sweat evaporates off your skin, your skin loses heat energy, and you feel cooler. How much evaporation takes place will depend on the air's relative humidity - i.e. how close the air is to being saturated. When RH is low, lots of water can evaporate before the air next to your body can become saturated, and so the body's cooling process is fairly efficient. When RH is high, however, evaporation is less efficient, since the air is closer to becoming saturated. In this case, the cooling process is not as efficient. [This same reasoning explains why your swamp cooler will work great in June and September, but not during July and August].
To take into account the effects of both heat and humidity on the human body, the heat index was developed. It expresses the heat stress on your body due to the combined effects of heat and humidity in terms of the equivalent air temperature. The equivalent temperature is then placed into one of four catergories, where category IV is the mildest and Category I is the worst. A typical Tucson day in July can easily reach a Category II heat index value. See the chart on page 139 to see what different values of temperature and RH produce for the heat index.
Relative Humidity and Clouds
Most of the time, air in the atmosphere is not saturated - i.e. the RH is less than 100 %. Recall from the above discussion that if you keep the amount of water vapor in the air constant and cool the air down, its RH will increase. Eventually, if you cool the air temperature down to the dew point temperature, the RH reaches 100 %, the air becomes saturated, and water vapor will begin to condense.
Clouds and fog are formed when air is cooled enough so that it beomes saturated and liquid water droplets begin to form. These droplets are typically very small (10 micrometers in diameter). This is small enough so that wind motions keep them aloft. Under certain conditions, these droplets may grow large enough that they begin to fall. This is how precipitation (rain, snow, hail, sleet) comes about. We will learn more about these processes next.