LAPSE RATES EXERCISE

Vocabulary

normal lapse rate, dry adiabatic lapse rate, wet adiabatic lapse rate, latent heat of vaporization; latent heat of condensation, windward, leeward

Behavioral Objectives

The student will be able to calculate when the air will be saturated given sufficient data.

The student will be able to calculate the equivalent sea level temperature, the temperature, or the altitude when given the other two.

The student will be able to determine the level of condensation and the temperature at point C on the mountain using the correct lapse rates given the base temperature, elevation, and moisture information.

Introduction

Temperature differences in the troposphere are a basic cause of many of the weather changes experienced at the surface of the earth. Several generalizations can be made concerning local temperature variations.

Temperatures decrease with increasing elevations. If a balloon were sent up, as it rose, the temperature would decrease fairly uniformly. The average or normal lapse rate says that the average change will be 3.5°F per 1000 feet elevation change. This change occurs partly due to the greenhouse effect and partly due to the lower density of the air. The normal lapse rate is especially useful to compare temperatures. For example, in order to accurately compare the temperature in New York City which is about at sea level (zero feet) with the temperature of the air of Denver, Colorado which is at about 5000' one would need to convert one of them so that they would both be at the same equivalent elevation so that the characteristics of the air masses would be similar. (See examples 1).

Air may rise for four reasons. Convectional lifting is caused by air at the surface being heated, thus, expanding, and rising. Frontal (cyclonic) lifting is caused where one air mass is forced to rise over another one. Convergence forces air to meet and rise because it can not move into the lithosphere. Orographic lifting occurs where air is forced to go over a landform barrier such as a mountain. All four of these cause the rising air to undergo pressure changes which also affect the temperature. When air is forced to rise, its temperature will decrease; and if air subsides, its temperature will increase.

When air is forced to move vertically, the average rate at which the temperature changes is 5.5°F per 1000'. This is called the dry adiabatic lapse rate. Recall, however that cold air can not hold as much water vapor as warm air and that cooling the air will cause it to approach and reach saturation. Also, remember that condensation is a warming process, releasing the latent heat of vaporization stored by evaporation. When the air is cooled below its dew point temperature, condensation occurs and adds heat to the air. For every 1000', 2.5°F of heat will be added. So, once condensation begins (or once the air cools below the dew point temperature) as the air rises, the temperature will drop 5.5°F per 1000' and 2.5°F of heat will be added by condensation so the result will be that the temperature will (-5.5°F + 2.5°F = 3.0°F) drop only 3.0°F per 1000'. This change in temperature of 3.0°F per 1000' while condensation is occurring is called the wet adiabatic lapse rate.

So as air rises until condensation begins, the air will cool at the dry adiabatic lapse rate of 5.5°F per 1000'; and after condensation begins, the air will cool at the wet adiabatic lapse rate of 3.0°F per 1000'. As the air comes down, its temperature will rise, so it will increase its ability to hold water vapor and so its relative humidity will be getting lower which means condensation will NOT occur. Therefore, the air will warm at the dry adiabatic lapse rate of 5.5°F per 1000'. (See example 2).

Weather greatly influences our everyday lives. Temperature and moisture are only two of the factors involved in the complex interaction which occurs between the atmosphere and the earth's surface. The more information that is obtained, the better will be the understanding and predictions about what the weather will be and how it will affect human activities.

Review Questions

As elevation increases, the temperature will _______________.

As elevation decreases, the temperature will _______________.

The normal lapse rate is _______________°F per_______________' and is used for _______________.

The dry adiabatic lapse rate is _______________°F per _______________' and is used when air is _______________ until _______________ begins.

The wet adiabatic lapse rate is _______________°F per _______________' and is used when air is _______________ while _______________ is occurring.

Answers: decrease; increase; 3.5, 1000, comparisons; 5.5, 1000, moving, condensation; 3.0, 1000, moving, condensation.

Examples 1

a. If the temperature were 76°F at sea level, what would the temperature of the air be at an airplane flying 4000 feet overhead?

This does not involve any vertical air movement, so the rate used would be the normal lapse rate. The temperature decreases with altitude.

4000 feet

- 0 feet

4000 feet difference in elevation

(simple math) four times the rate for 1000' = 4000'

3.5 x 4 = 14.0°F change in temperature

76°F - 14°F = 62°F at 4000'

OR (algebra)

3.5°F = X
1000 4000'

1000x = 3.5°F (4000')

1000x = 14000

x = 14°F

The temperature changes 14°F and drops.

76°F - 14°F = 62°F at 4000'.

b. The temperature in Denver, Colorado, elevation 5000' is 53°F and the temperature in New York City at sea level is 68°F. Does the air in New York City actually contain more heat than the air in Denver?

5000' - 0 = 5000' change in elevation

5000' / 1000' = 5 times the rate

No actual vertical movement of the air occurs; this is a comparison. The normal lapse rate is used.

5 x 3.5°F = 17.5°F

APPROACH A

Convert the temperature of New York to the temperature at 5000'.

68°F - 17.5°F = 50.5°F is the temperature at 5000' above New York.

Denver is 53°F. New York's air does not contain more heat.

APPROACH B

Convert the temperature of Denver to what it would be at sea level.

53°F + 17.5°F = 70.5°F is the equivalent sea level temperature.

New York is 68°F. Denver contains more heat in its air than New York.

On all of the mountains used by Dr. Hill, the wind will be blowing across the mountain from A to X to B to C. See basic mountain and also see Lapse Rate Summary Diagram Point X represents the point where condensation begins. Note: The positioning of point X on the mountain does not represent its actual location as it may be at a higher elevation than point B, lower than point A, either at A or B, or anywhere in between points A and B.

Example 2

A = 3000'; B = 9000'; C = 3000' The temperature at point A is 79°F, and the dew point temperature is 57°F. What would be the equivalent sea level temperature of C?

From A to X the air cools 79°F -57°F = 22°F at the dry adiabatic lapse rate. 22/5.5 = 4 times or 4000' elevation change. X is at an elevation of (3000' + 4000' =) 7000'. From X to B the air cools at the wet adiabatic lapse rate. 9000' - 7000' = 2000' elevation change. 2000'/1000 = 2 times the rate. 2 x 3.0 = 6°F change. 57°F - 6°F = 51°F at B.

From B to C it warms at the dry adiabatic lapse rate. 9000' - 3000' = 6000'/1000' = 6 times the rate. 6 x 5.5°F = 33°F change. 51°F + 33°F = 84°F at C. (Note that this is warmer than at A.)

C is at 3000', and the air can not physically move to sea level. Thus, this will be the equivalent sea level temperature. Since it is a comparison and involves no vertical air movement, it uses the normal lapse rate. 3000' - 0'(sea level) = 3000' elevation change. 3000'/1000' = 3 times the rate. 3 X 3.5°F = 10.5°F change. 84.0°F + 10.5°F = 94.5°F is the equivalent sea level temperature of C.

Problems

1. Complete the following table.

elevation temperature sea level temperature
1000' _______________ 77°F
6000' 84°F _______________
___________ 28.75°F 34°F
10,000' _______________ 46°F
200 63°F _______________

2. A = 1000', B = 7000', C = 3000'. The temperature at A is 82°F and this air contains 5.7 grains of water vapor. Condensation will begin at _______________ degrees. This point is represented by X and is at an elevation of _______________ feet. The temperature at B is _______________. The temperature at C is _______________°F. The equivalent sea level temperature of the air at C would be _______________°F.

3. A = 2000', B = 19,000', C = 7000'. The equivalent sea level temperature of A is 87°F and the dew point temperature is 47°F. The temperature at A is _______________ degrees. The elevation of X, the height at which the cloud base will occur, is _______________'. The temperature at B is _______________°F. The temperature at C is _______________°F. The equivalent sea level temperature of the air at C would be _______________°F. If one assumes that when the air temperature reaches 32°F, snow falls, the height of the snowline on the windward side of the mountain would be _______________.

4. Use mountain chain A. A = 1000', B = 4000', C = 1000', D = 8000', E = 2000', F = 5000', G = 1000'

a. If the temperature at A is 68°F, the sea-level temperature would be _______________°F.

b. If condensation occurs, the air temperature at C is _______________ (the same, colder, warmer) than at A because _______________.

c. If condensation on Mt. X begins when the air is cooled to 50°F and the air at B is 40°F, the dew point on Mt. Y will be _______________°F. In this case, will condensation occur on Mt. Z? _______________ Why?_______________

d. If the dew point is not reached as the air moves over these mountains, the air temperature at G will be _______________(the same, colder, warmer) than the air at A.

e. If the air becomes saturated at some time as it blows over the mountains, the temperature at G will be _______________(the same, colder, warmer) than the air at A.

f. Which mountain peak will most often be covered by clouds?_______________

Answers: 1. 73.5°F, 105°F, 1500', 11°F, 63.7°F; 2. 60, 5000, 54, 76, 86.5; 3. 80, 8000, 14, 80, 104.5, 13,000; 4. a. 71.5°F; b. warmer, latent heat of condensation; c. 40°F, no, It does not reach the dew point temperature.; d. the same; e. warmer; f. Mt. Y.

More Practice

Fill in the table below.

elevation temperature sea level temperature
8000' 42°F _______________
______________ 45°F 59°F
10,000' _______________ 98°F
5,000' 25.5°F _______________
_______________ 46°F 67°F
2,000' _______________ 81°F
4000' _______________ 55°F
6000' 68°F _______________
___________ 29F 71
3000' _______________ 48.5°F
9000' 50°F _______________
1000' _______________ 86.5°F
4000' 44°F _______________
6000' _______________ 30°F
10,000' 35°F _______________
2,000' 51°F _______________
8,000' _______________ 68°F

Answers: 70°F, 4000', 63°F, 43°, 6000', 74°F, 41°F, 89°F, 12,000', 38°F, 81.5°F, 83°F, 58°F, 9°F, 70°F, 58°F, 40F.

1. A = 1000', B = 14,000', C = 2000'. The temperature at A is 83°F and the air contains 4.1 grains of water vapor. Condensation will begin at _______________°F and an elevation of _______________ feet. The temperature at B is _______________°F and at C is _______________°F. The equivalent sea level temperature of the air at C is _______________.

2. A = 4000', B = 17,000', C = 5,000'. The equivalent sea level temperature is 92°F and the dew point is 45°F at A. The temperature at A is _______________F. The cloud base will occur at _______________ feet. The temperature at B is _______________°F and at C is _______________°F. If one assumes that when the air temperature reaches 32°F snow falls, what would be the height of the snowline on the windward side of the mountain? _______________

3. A = 2000', B = 12,000', C = 6000'. The equivalent sea level temperature at A is 80°F. The air contains 2.9 grains of water vapor. The temperature at A is _______________°F. The dew point temperature is _______________°F and occurs at an elevation of _______________ feet. The temperature of B is _______________°F. The temperature of C is _______________°F. The equivalent sea level temperature of C is _______________°F.

4. The air temperature is 64°F and the elevation is 4000'. The equivalent sea level temperature would be _______________°F.

5. The air temperature is 82°F and the elevation is 0'. The equivalent temperature at 6000' would be _______________ degrees.

6. The equivalent sea level temperature is 70°F and the air temperature is 63°F. The elevation is _______________ feet.

7. A= 3000'; B = 9000'; C = 5000'; D = 3000' and is to the leeward side of point C.

a. The temperature at A is 68°F and the dew point is 57°F. The temperature at B will be _______________°F.

b. The temperature at A is 92°F and the air contains 8.0 grains of water vapor. The temperature at B will be _______________°F.

c. The temperature at B is 58°F and the air contains 2.9 grains of water vapor. The temperature at C is _______________°F.

d. The temperature at A is 71°F and the air contains 5.7 grains of water vapor. Condensation will begin at _______________ feet.

e. The temperature at A is 52°F and the dew point is 41F. If one assumes that when the air temperature reaches 32°F snow falls, the height of the snowline on the windward side of the mountains would be _______________.

f. If condensation occurs between point A and point B, the temperature at D would be _______________ (the same, warmer, colder) than the actual temperature at A.

8. A = 4000', B = 8000', C = 6000'. The equivalent sea level temperature of the air at A is 70°F and the dew point temperature is 23°F. The temperature at A is _______________°F. The elevation of X is _______________ feet. The temperature at B is _______________°F, and at C is _______________°F. The equivalent sea level temperature of C is _______________°F.

9. A= 2000', B = 10,000', C = 4000'. The equivalent sea level temperature of the air at A is 89°F. The air contains 5.7 grains of water vapor. The temperature at A is _______________°F, the temperature at X is _______________°F, the elevation of X is _______________ feet, the temperature at B is _______________°F, the equivalent sea level temperature of the air at B is _______________°F, the temperature at C is _______________°F, and the equivalent sea level temperature of the air at C is _______________°F.

10. A = 6000', B = 14,000', C = 2000'. The temperature at A is 73°F and it contains 2.9 grains of water vapor. The equivalent sea level temperature of the air at A is _______________°F, the temperature of the air at X is _______________°F, the elevation of X is _______________ feet, the temperature at B is _______________°F, the temperature of C is _______________°F, and the equivalent sea level temperature is _______________°F.

11. A = 2000', X = 4000', B = 9000', C = 3000'. The equivalent sea level temperature of the air at A is 68°F. the temperature at A is _______________°F, the dew point temperature is _______________°F, the temperature at B is _______________°F, the temperature at C is _______________°F, and the equivalent sea level temperature of C is _______________°F.

mountain chain B--A=2000'; B=4000'; C=2000'; D=8000'; E=2000'; F=5000'; G=2000'; H=10,000'; I=2000'; J=9000'; K=2000'

12. Use mountain chain B to answer the following questions. Circle the correct answer or fill in the blanks.

a. If condensation does not occur, the air temperature at C will be (the same as, colder than, warmer than) A.

b. If condensation occurs on Mt. V, the air temperature at C will be (the same as, colder than, warmer than) A.

c. If condensation on Mt. V. begins when the air is cooled to 50°F, the air at B is 40°F, the dew point on Mt. W will be _______________F.

d. If the dew point is NOT reached as the air blows over these mountains, the temperature at K will be (the same as, warmer than, colder than) the air at A.

e. If the air becomes saturated at some time as it blows over the mountains, the temperature at I will be (the same as, colder than, warmer than) the air at A.

f. Which mountain peak will most often be covered by clouds? _______________

g. If the air becomes saturated as it moves from A to B, will condensation occur on Mt. W?_______________ The temperature at E will then be (the same as, warmer than, colder than) the temperature at C. The temperature at G will be (the same as, colder than, warmer than) the temperature at E. The dew point on Mt. Y will be the temperature at point _______________. Condensation (will, will not) occur on Mt. Y. The temperature at I will be (the same as, warmer than, colder than) the temperature at G. The temperature at K will be (the same as, warmer than, colder than) the temperature at I. condensation (will, will NEVER) occur on Mt. Z, if the wind direction remains as indicated.

h. If the wind direction reverses, the dew point temperature will be determined most often by point _______________. If condensation occurs on Mt. Z, condensation will also occur on (Mt. V., Mt. W., Mt. X., Mt. Y, NONE of these). If condensation does not occur on Mt. Z, condensation may occur on (Mt. V, Mt. W., Mt. X, mt. Y, Mt. Z, NONE of these). If condensation occurs on Mt. Y., it will occur on (Mt. V., Mt. W., Mt. X, ALL of these, NONE of these). If condensation does not occur on Mt. Y, it will occur on (Mt. V, Mt. W, Mt. X, NONE of these).

13. A = 4000' and 73°F, X = 10,000', B = 16,000', C = 4,000'. The temperature at X is _______________°F. The temperature at B is _______________°F. The temperature at C is _______________.

14. A = 2,000' and 88°F, X = 6000', B = 10,000', C = 4,000'. The temperature at X is _______________°F, at B is _______________°F, and at C is _______________°F.

15. A = 6000' and 90F, X = 79°F, B = 10,000', C = 2,000'. The difference in temperature between point A and point X is _______________°F. The elevation of X is _______________ feet. The temperature of B is _______________°F and at C is _______________°F.

16. A = sea level and 79F, X = 57F, B = 14,000', C = 2,000'. The difference in temperature between point A and point X is _______________°F. The elevation of X is _______________ feet. The temperature of B is _______________°F and of C is _______________°F.

17. A = 4000' and 60°F, X = 27°F, B = 8000', C = 4000'. The difference in temperature between point A and point X is _______________°F. The elevation of X is _______________ feet. The temperature of B is _______________°F and of C is _______________°F.

18. A = 8000', B = 20,000', C = 6000'.

a. The temperature at A is 72°F and the elevation of X is 12,000'. What is the dew point temperature? _______________°F

b. The temperature at A is 85°F and the temperature at X is 41°F. What is the elevation of X? _______________ feet

c. The temperature at X is 62°F and the elevation of X is 10,000'. What is the temperature at B? _______________°F

d. The temperature at B is 17°F. What is the temperature at C? _______________°F

Answers: 1. 50, 7000, 29, 95, 102; 2. 78, 10,000, 24, 90, 14,333 1/3; 3. 73, 40, 8000, 28, 61, 82; 4. 78; 5. 61; 6. 2000; 7. a. 45, b. 64, c. 80, d. 5000, e. 8000, f. warmer; 8. 56, 10000, 34, 45, 66; 9. 82, 60, 6000, 48, 83, 81, 95; 10. 94, 40, 12,000, 34, 100, 107; 11. a. 61, 50, 35, 68, 78.5; 12. a. the same as; b. warmer than, c. 40; d. the same as; e. warmer than; f. Mt. Y; g. yes, warmer than, the same as, D, will, warmer than, the same as, will NEVER; h. H, Mt. Y, Mt. Y, NONE of these, NONE of these; 13. 40, 22, 88; 14. 66, 54, 87; 15. 11, 8000, 73, 117; 16. 22, 4000, 27, 93; 17. 33, 10,000, 38, 60, 18. a. 50, b. 16,000, c. 32, d. 94.