ATMO 336 - Weather, Climate, and Society

Fall 2008 - Homework #2

Answer the following questions on a separate sheet of paper. Homework answers squeezed onto this page will not be accepted. If you need to calculate an answer, you must show your work. To answer question 2, you will need to refer to the skew-T diagrams located under the homework link on the course web page. Tables of saturation mixing ratios were provided with an in-class handout. The table in Fahrenheit is also provided under the homework link on the course web page. Use the heat index and wind chill tables (provided in lecture notes page entitled "Temperature, humidity, wind, and human comfort" to help answer questions 4 and 5. Make sure you read and answer all the parts to each question!

1. 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. (Round the elevation to 9000 meters). We will look at how air temperature, pressure, and density change on your way up.

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 notes page entitled "Vertical variation of temperature, pressure, and density in the atmosphere."

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

(c) 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). Hint: you should mention air density in your answer.

2. You must use the two skew-T diagrams, labeled as fig2a and fig2b located under the homework link on the class web page to answer this question. Both diagrams were drawn based on data measured at Tucson. One figure corresponds to data measured at 0000 UTC (or 00Z) on September 9, 2008 and the other to 1200 UTC (or 12Z) on September 9, 2008.

(a) What was the local Tucson date and time corresponding to the two UTC times and dates specified above?

(b) Determine which skew-T figure was based on measurements taken at 00Z and which skew-T figure was based on measurements taken at 12Z. Briefly explain how you arrived at your answer.

(c) Fill in the missing values in the table below by reading values from the skew-T chart, labeled as fig2a.Re-write the table on your own paper. Do not squeeze answers into the table below.

(d) Looking at the skew-T chart, labeled as fig2a, it appears that the weather balloon went through a cloud. Roughly estimate the height above sea level of the bottom and top of the cloud. No need to try to figure out exact heights. Hint: find where the relative humidity is close 100%. What is the approximate air temperature in the middle of the cloud?

Air Pressure (mb)	Altitude Above Sea Level (m)	Air Temperature (°C)	Dew Point Temperature (°C)	Wind Direction	Wind Speed (knots)
200	12380	-51	-65	West	55
250
300
400
500
700
850	1495	24	9	Southeast	5

3. On a day last summer, the following conditions were measured on the UA campus.

n At 8 AM: air temperature, T = 75 °F; dew point temperature, T_d = 50 °F.

n At 11 AM: air temperature, T = 85 °F; dew point temperature, T_d = 55 °F.

n At 2 PM: air temperature, T = 95 °F; dew point temperature, T_d = 60 °F.

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

(b) At which time of day is the relative humidity lowest? At which time of day was the concentration of water vapor in the atmosphere highest? Hint: the answer to these two questions is the same.

(c) To many people, who have not taken this class, the answer to the questions in part (b) seems counterintuitive. Explain how it is possible that the lowest relative humidity can occur at the same time that the water vapor content is highest?

4. On a summer day, the conditions measured at Tucson, Arizona and New Orleans, Louisiana are given

Tucson, Arizona

Air Temperature	100° F
Relative Humidity	15 %

New Orleans, Louisiana

Air Temperature	90° F
Relative Humidity	60 %

(a) Using the heat index chart provided with the course lecture notes, find the heat index for the two cities. Which location is most stressful to the human body? Compare the rate of heat loss from the human body at these two locations.

(b) Compute the dew point temperatures for the two cities (you may select the closest value contained in the saturation mixing ratio table). Which city has the higher concentration of water vapor in the air? How do you know?

5. On a winter day, conditions measured at Fairbanks, Alaska and West Yellowstone, Montana are given

Fairbanks, Alaska

Air Temperature	0° F
Wind Speed	5 MPH

West Yellowstone, Montana

Air Temperature	15° F
Wind Speed	40 MPH

(a) Using the wind chill chart provided with the course lecture notes, find the wind chill equivalent temperature for the two cities. Which location is most stressful to the human body? Compare the rate of heat loss from the human body at these two locations.

(b) Explain why the conditions specified above would be more dangerous for people who are wearing wet clothing. Assuming people in both cities are outside in wet clothing, how might your answers to the last two parts of 5(a) change? Explain.

6. 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, the air is cooled because energy is removed from the air in order to evaporate water. Thus, air that has moved through the wet pad is both cooler and contains more water vapor than the outdoor air.

The drop in temperature between the outside air and the air that cones out of the evaporative cooler 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, which was not discussed in lecture and is defined here, 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. Note that the wet bulb temperature is not the same as the dew point temperature.

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 of water?)