ATMO 336 - Weather, Climate, and Society

Spring 2007 - Homework #3

Due in class on Tuesday, February 13^th

Answer the following questions on a separate sheet of paper. If you need to calculate an answer, you must show your work. You will need to use the table of saturation mixing ratios below to help answer questions 1-2. (The table below is in Fahrenheit; you cannot use table 4.1 included in the in-class handout because it is in Celsius). Use the heat index and wind chill tables (provided in lecture notes) to help answer questions 3-4. Make sure you read and answer all the parts to each question!

Temperature (ºF)	Sat. Mixing Ratio (g/kg)	Temperature (ºF)	Sat. Mixing Ratio (g/kg)
5	1.21	55	9.32
10	1.52	60	11.19
15	1.89	65	13.38
20	2.34	70	15.95
25	2.88	75	18.94
30	3.54	80	22.43
35	4.33	85	26.48
40	5.28	90	31.16
45	6.40	95	36.56
50	7.74	100	42.78

1. On a day in winter 2005, the following conditions were measured on the UA campus

n At 8 AM: air temperature, T = 45° F; dew point temperature, T_d = 25° F.

n At 11 AM: air temperature, T = 60° F; dew point temperature, T_d = 25° F.

n At 2 PM: air temperature, T = 70° F; dew point temperature, T_d = 25° F.

(a) Compute the relative humidity for each of the times/conditions specified above.

(b) Explain why the relative humidity changed the way it did from 8 AM through 2 PM. How did the water vapor content in the air change between 8 AM and 2 PM?

2. Values of air temperature and relative humidity are given below for Presque Isle, Maine and Tucson, Arizona as observed on a day in spring 2004.

Presque Isle, Maine

Air Temperature	35° F
Relative Humidity	100 %
Weather Conditions	Rain

Tucson, Arizona

Air Temperature	90° F
Relative Humidity	25 %
Weather Conditions	Sunny

(a) What are the approximate dew point temperatures at the two locations?

(b) Of these two locations, which has the higher concentration of water vapor in the air? How do you know? Explain how a desert location with a low relative humidity can actually have a higher water vapor content than a location where the relative humidity is 100% with rain falling?

3. On a day in summer 2004, the measured conditions in Tucson, Arizona and Charleston, South Carolina were:

Tucson: Air temperature = 105° F, Relative Humidity = 10 %

Charleston: Air temperature = 95° F, Relative Humidity = 50 %

(a) Using the heat index chart provided with the course lecture notes (covered in class on Feb. 8), find the heat index for the two cities. Compare the rate of heat loss from the human body at these two locations.

4. On a day in winter 2005 the measured conditions in Flagstaff, Arizona and West Yellowstone, Montana were:

Flagstaff: Air temperature = 0° F, Wind speed = 20 MPH

West Yellowstone: Air temperature = -10° F, Wind speed = 5 MPH

(a) Using the wind chill chart provided with the course lecture notes (covered in class on Feb. 8), determine the wind chill equivalent temperature for the two cities. Compare the rate of heat loss from the human body at these two locations.

5. Evaporative cooling is one of the most ancient and one of the most energy-efficient methods of cooling a home. It long has been regarded as environmentally "safe," since the process uses no ozone-depleting chemicals, and demands one-fourth as much energy as refrigeration during the peak cooling months of the year. In dry climates such as Tucson, evaporative cooling can be used to inexpensively cool large homes. Locally, these devices are often referred to as “swamp coolers”.

The most common form of residential evaporative cooling uses a vertical pad of absorbent cellulose fiber, a system for delivering water to the pad to keep it soaked with water, and a fan to draw air through the porous pad. As warm, dry outside air is drawn through the wet pad, water evaporates into the air, and the air gives up its heat. In other words, energy is removed from the air in order to evaporate water. Thus, air that has moved through the wet pad is cooler than the outdoor air and contains more water vapor than the outside air.

The drop in temperature depends on how much water can be evaporated into the air. This is obviously a function of relative humidity. When the relative humidity is low, the temperature drop can be large. However, when the relative humidity is high, the temperature drop will be small (and the swamp cooler doesn’t help much).

The wet bulb temperature is the lowest temperature to which air can be cooled by evaporating water into it. This is the theoretical lower limit for the temperature of the air that comes out of an evaporative cooler.

Explain the following statements:

(a) When the relative humidity is 100%, the air temperature, the dew point temperature, and the wet bulb temperature are identical. Explain.

(b) When the relative humidity is less than 100%, the dew point temperature and the wet bulb temperature are both lower than the air temperature. Explain.

(c) When the relative humidity is less than 100%, the wet bulb temperature will always be higher than the dew point temperature. Explain. (Hint: What is happening to the water vapor content and dew point temperature of the air as it is being evaporatively cooled? At what point does it become impossible to further cool air by evaporation?)

6. Suppose you were going to walk from the ocean near Calcutta, India up to the top of Mount Everest at 8846 meters above sea level. We will round off the elevation to 9000 meters. We will look at how air temperature and air pressure change on your way up, using the table below

Elevation (meters)	Fraction of way up by altitude	Air Temperature	Air Pressure	Percentage of the atmosphere below you by weight
0	At bottom	30° C	1000 mb	0 %
3000	1/3	?	700 mb	?
6000	2/3	?	500 mb	?
9000	At top	?	330 mb	?

(a) Estimate the air temperature at 3000, 6000, and 9000 meters. The information you need to do this is contained on the lecture page entitled “Temperature, pressure, and density of the Atmosphere” (covered on Jan. 18).

(b) Compute the percentage of the atmosphere below 3000, 6000, and 9000 meters (based on weight).

(c) Explain why air pressure decreases as you move upward in altitude.

(d) Explain why the rate of decrease of air pressure is not constant with increasing altitude, i.e., it drops by 300 mb over the first 3000 meters of the climb (from 0 m to 3000 m), 200 mb over the next 3000 meters of the climb (from 3000 m to 6000 m), and 170 mb over the last 3000 meters of the climb (from 6000 m to 9000 m).

7. Let’s start with two identical columns of air that each extend from sea level upward to the top of the atmosphere. The air temperature at the bottom of each column is 0° C and the air pressure at the bottom of each column is 1000 mb. Suppose one air column is heated so that the air temperature at the bottom of the column is now 20° C.

(a) If no air is allowed to enter or leave the heated air column, explain why the air pressure at the bottom is still 1000 mb.

(b) Which air column now has a higher number density at the bottom of the column? Explain.

(c) Suppose these two air columns are taken from two different air masses, a warm air mass (air temperature just above the ground surface of 20° C) and a cold air mass (air temperature just above the ground surface of 0° C). If these two air masses slam into each other, which air mass will be forced upward? Explain why.