February 27, 2008

Energy Transfer via Convection (Continued)

o Moist Convection accounts for energy removed due to evaporation of water, liquid à gas (usually from near the ground surface). This energy is later delivered where the water vapor (gas) condenses, gas à liquid (typically during cloud formation). The net effect is that energy is removed from near the ground surface and later released high up in the atmosphere.

§ Draw a figure to help explain this process.

§ Because so much energy is involved in phase changes of water between the liquid and gaseous phases, a tremendous amount of energy is transferred from near the ground up into the atmosphere via moist convection. In Earth’s climate, over 3 times more energy is transferred from the surface to the atmosphere due to moist convection than is transferred via dry convection and conduction.

Overview of the Hydrological Cycle on Earth (Chapter 4)

n Put up figure 4.1 from textbook.

n The cycling of water from the oceans to the atmosphere to precipitation on land and eventually running back to the oceans is absolutely essential for life on land to exist.

A closer look at the physical processes of evaporation and condensation

n In order to describe the physics of these processes, we need some way to specify the water vapor content of the atmosphere. There are many ways to do this and we will use a few of them in this class. The first is something called vapor pressure.

n Vapor pressure is the pressure (force/area) exerted by water vapor molecules alone. The higher the concentration of water vapor molecules (number density), the higher the vapor pressure. The average air pressure at sea level is about 1013 millibars (mb). If the total air pressure is 1013 mb and water vapor makes up 1% of the air molecules, then the vapor pressure is 1% of 1013 mb or 10.13 mb. Water vapor is a trace gas in the atmosphere of Earth -- the maximum vapor pressure is never more than about 40 mb. For now the important concept is that vapor pressure is one way to keep track of the amount of the gas water vapor. The higher the vapor pressure, the greater the amount of water vapor in the air.

n We will use an in-class handout as a visual aid to assist in understanding. We will also need the following definitions and background material:

o The rate of evaporation is the number of water molecules that change phase from liquid to gas per second. This rate depends mainly on the temperature of the liquid water surface … the higher the temperature, the faster the rate.

o The rate of condensation is the number of water molecules that change phase from gas to liquid per second. This rate depends mainly on the vapor pressure … the higher the vapor pressure, the faster the rate.

o The processes of evaporation and condensation go on simultaneously. They also occur over a wide range of temperatures. The latent heat diagram that I drew earlier is a bit misleading in that it can lead you to think that in order for water to evaporate, we need to heat the liquid water up to 100° C. But this is not true. Water is evaporating all the time at lower temperatures. You can convince yourself of this by setting out a glass of water. Eventually it will evaporate even though it was never heated to its boiling point.

o Use handout to describe how water behaves. We can make the following points:

§ In a closed system (like figure 4.5 in the handout), the air above a liquid water surface will become saturated with water vapor. We can measure the saturation vapor pressure at various temperatures in a lab.

§ Saturation is the maximum amount of water vapor that can exist in the air (i.e., the capacity for water vapor). As air temperature increases, the saturation vapor pressure increases sharply.

· Warm air can hold more water vapor than cold air

§ Look at and explain figure 4.5 from textbook

· Briefly describe what it means for water to boil. Water is said to boil when the saturation vapor pressure of the water is equal to the surrounding air pressure. Using figure 4.5 and applying what we know about air pressure (it decreases with increasing altitude), we can understand why water will boil at a lower temperature at high elevations, e.g., on top of a mountain.

n Evaporation and Condensation in the atmosphere

o Near the Earth's surface, the vapor pressure is usually less than the saturation vapor pressure. (NOTE: the actual vapor pressure of the air can vary from zero up to the saturation vapor pressure). Therefore, the rate of evaporation is greater than the rate of condensation, i.e., liquid water near the Earth's surface is continually evaporating (changing phase from liquid to gas). You can easily convince yourself that this is true by leaving out a glass of water. All of the liquid will eventually evaporate. The reason the air near the ground does not reach saturation is because after the water evaporates, the water vapor is able to move away from the surface. It is not trapped as in the closed experiment described above.

o Once water has evaporated it becomes part of the gases that make up the atmosphere. When air rises upward, it cools (the reason rising air cools will be explained later). As air cools, its saturation vapor pressure decreases, in other words, the maximum amount of water vapor that the air can hold decreases. If the air rises high enough and cools sufficiently, it will not be able to hold all the water vapor it contains. When this happens, water vapor must condense back to liquid water. This is how clouds form. Clouds are composed of tiny droplets of liquid water (and possibly ice). Water vapor is an invisible gas and cannot ever be seen. If you see it, e.g., clouds, steam, your breath on a cold day, it must be liquid water droplets. We will talk more about clouds soon.

Water Vapor in the Atmosphere

n It is important to be able to specify how much water vapor is in the air. We have already seen one way to specify the amount of water vapor in the air, that is, vapor pressure. We will now add the concepts of relative humidity and dew point temperature.

n In class, we will sometimes use the concept of an air parcel. An air parcel is an imaginary 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 extremely important in describing cloud and thunderstorm formation. For one thing, we will eventually want to keep track of the relative humidity in an air parcels as it moves up and down in the atmosphere.

n The relative humidity (RH) 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 that could be in the air, which we call the saturation amount or the water vapor capacity of the air. Remember the water vapor capacity depends strongly on the air temperature (saturation vapor pressure).

o Relative Humidity = (water vapor content) / (water vapor capacity)

o For example, if the relative humidity is 50%, it means that the air contains one half of its capacity (or saturation amount) for water vapor. If the relative humidity is 100%, it means the air contains its capacity (or saturation) amount of water vapor.

o One way to express or compute relative humidity is to take the ratio of the actual vapor pressure divided by the saturation vapor pressure (capacity). However, we are going to use a unit called mixing ratio to do this.

n The mixing ratio (U) is defined as the actual mass of water vapor in a parcel (in grams) divided by the mass of the remaining air in the parcel (in kilograms). The biggest reason to use mixing ratio is that as long as there is no phase change of water in a parcel, the mixing ratio does not change as a parcel is moved up and down in the atmosphere; however, vapor pressure in a parcel does change as the parcel is moved up or down.

n The saturation mixing ratio (U_S) is defined as the mass of water vapor that must be in a parcel for it to be saturated with water vapor (in grams) divided by the mass of the remaining air in the parcel (in kilograms).

n Using the definitions of mixing ratio (U) and saturation mixing ratio (U_S), we can now determine relative humidity (RH) as

o RH = U / U_S

o Go over Table 4.1 (Saturation Mixing Ratio) on in-class handout. Describe what happens in a closed system.

o Do a few examples for computing Relative Humidity using the concept of mixing ratio.

n Most people use Relative humidity to describe the water vapor content of the air, but it is widely misunderstood. Relative humidity in itself does not indicate the actual amount of water vapor in the air because it depends on temperature. It only tells you how close the air is to being saturated. For example, an air parcel at a temperature of 10°C with RH = 100% contains the same concentration of water vapor as an air parcel at a temperature of 20°C with RH = 50%. You should be able to convince yourself of this by using the Table 4-1 from the class handout.

o In fact RH can be changed in two ways:

§ Change the amount of water vapor in a parcel (changes U)

§ Change the air temperature in the parcel (changes U_S)

n The dew point temperature (or dew point) (T_d) is the temperature to which an air parcel would have to be cooled for the parcel to become saturated with water vapor.

o 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?

o Unlike RH, the dew point temperature does indicate the actual amount of water vapor in the air … the higher the dew point, the higher the water vapor content of the air.

o We will also use table 4.1 from the class handout to perform calculations involving the dew point temperature.

§ Describe the correspondences between

· Air temperature and saturation mixing ratio

· Dew Point Temperature and mixing ratio

§ Go over some example calculations

o The following statements should make sense to you:

§ 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