ATMO 336 - Weather, Climate, and Society

Fall 2009 - 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 6 and 7. 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 page entitled “Vertical variation of temperature, pressure, and density in the atmosphere” from September 1.

(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 8, 2009 and the other to 1200 UTC (or 12Z) on September 8, 2009.

(a) What is the local Tucson date and time corresponding to 00 Z September 8, 2009 and 12 Z September 8, 2009 ?

(b) Determine which skew-T figure (2a or 2b) 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 fig2b. Re-write (or cut and paste) the table on your own paper. Do not squeeze answers into the table printed below.

(d) Looking at the skew-T chart, labeled as fig2b, 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	12320	-55	-67	West	15
250
300
400
500
700
850	1497	22	13	Northwest	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. Consider a drinking glass full of ice water (liquid water and lots of ice cubes) that is at a temperature of 32° F (0° C). The surrounding air is still (no wind), the air temperature is 60° F, and the dew point temperature is 45° F. Describe two processes that will act to add energy (or heat) to the ice water through the sides of the glass (you do not need to discuss energy or heat exchanges through the top and bottom of the glass of ice water). Even though heat is being added, you notice that the temperature of the ice water inside the glass remains steady at 32° F. Explain.

5. When rain first begins to fall, it is common for the air temperature in the lower atmosphere (just above the ground) to drop. Explain how the onset of rain can cause the air temperature to drop. (Hint: consider the environmental conditions through which the rain drops fall.) Suppose the air temperature is 50° F and the dew point temperature is 40° F just as rain starts to fall. After 10 minutes, the air temperature falls to 45° F and remains steady even though rain continues to fall. Explain why the air temperature does not cool down to 40° F, the dew point temperature measured before the rain began to fall.

6. 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?

7. 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.