HOMEWORK 4 ANSWER SHEET

1) a. The temperature at Biff's houseboat is 70deg.F. The lapse rate is 3.6deg.F per 1000 ft. increase in elevation. So, temperature as a function of height looks like:

T(z) = T(0) - (Lapse Rate) x z

where z is height above sea level, and z = 0 corresponds to sea level (Biff's houseboat). So,

T(5000 ft) = 70deg.F - 3.6 (deg.F/1000 ft) x 5000 ft = 52deg.F

b. Biff's stay in the mountains will be more comfortable if it was cloudy for the night (provided it doesn't rain). Clouds trap longwave radiation well, so they act to keep the surface warm through enhancing the greenhouse effect. During the night, the earth emits LW radiation towards space. On a clear night, some of that LW radiation is absorbed by atmospheric greenhouse gases, but much is allowed to escape to space. However, on a cloudy night, the clouds absorb much of the LW radiation that typically escapes to space. Half of that is reradiated back to the surface, which acts to keep Biff warm during the night.

2) a. Figure A looks most like the profile of temperature with height at the South Pole in December. During the day, shortwave radiation heats up the surface of the earth, which in turn radiates away to the rest of the atmosphere. This heats the atmosphere from below, which is why the troposphere shows a decrease in temperature with height. During December at the South Pole, the sun is constantly up, so the temperature profile should look like typical daytime temperature profile.

b. Figure C looks most like the profile of temperature with height at the South Pole. During the night, the earth's surface emits radiation very efficiently, cooling rapidly. The air near the surface of the earth conducts some of its heat to the surface, which in turn radiates that energy back to space. So, the air near the surface cools from below, which causes a temperature inversion. This is on page 69 of the book.

3) a. If the tilt of the earth's axis were 0deg. (instead of 23.5 degrees), the diurnal cycle would most seriously affect the temperature on the earth. If the earth's tilt were 0deg., every latitude would receive 12 hours of daylight, and 12 hours of night, every day of the year. So, the length of day would not change, nor the angle of incidence of the sun (except that associated with the diurnal cycle). This means that the only way to vary the amount of radiation received at the surface would be through the diurnal cycle.

b. If the tilt of the earth were 90deg., the seasonal cycle would most seriously affect the temperature on the earth. If the earth's tilt were 90deg., there would be no diurnal cycle at the solstices, so the only way the amount of received radiation could change would be through the revolution of the earth around the sun.

c. January is colder than July due to the tilt of the earth. Although the earth is closer to the sun in January, the sun's incoming radiation is incident at a more oblique angle, due to the tilt of the earth. Thus, the incident radiation is more diffuse (spread out over a larger area), and must travel through a larger section of the atmosphere before reaching the surface (more chance for radiation to be scattered or reflected). Likewise, the tilt of the earth affects the length of day. During January, the length of day is shorter than during July, so the daily averaged incident solar radiation is less.

4) a. Page 81 - 82 has a description of the sort of place one would put a thermometer. Usually, thermometers are placed inside a instrument shelter, which is painted white, and placed in grass somewhere. The box should be well ventilated to allow air to pass through easily.

b. If the thermometer is in the direct sunlight it will read a higher temperature than it should. Likewise, if the thermometer were placed over asphalt it would show a larger diurnal variation that if it were placed over regular ground. There are many possible answers here.

c. The thermometer that was placed in the valley should show a larger diurnal cycle than the thermometer on the hill, due to the possibility of radiative inversions. As the ground cools, air next to the side of the hill will tend to sink down the hill to the valley, filling the valley with cool air. During the day, the opposite effect occurs. Due to the lapse rate in the troposphere, one might expect a little cooler temperature (on average) on the top of the hill than at the bottom of the valley.

5) a. The relative height of the clouds is more readily obtained through the radiometer observations.

b. Warmer objects emit more radiation. We know that energy is proportional to the fourth power of temperature, so the one emitting more energy is warmer. As the temperature decreases with increasing height in the troposphere, the colder clouds will be high clouds, and the warmer clouds will be low clouds. So, if the clouds over the ocean are emitting more radiation than those over land, the clouds over the ocean are lower than those over land.

c. Because low clouds have a temperature very close to land, it is sometimes difficult to make distinctions between low clouds and land using IR photography. To determine the horizontal structure, it would be best to rely on visual observations.

6) a. On map.

b. The land was lighter than the ocean, so it is emitting less radiation (look at the color of space for a reminder). Thus, the land was cooler than the ocean.

c. This picture was taken in November, when the land is not drastically colder than the ocean. As the land heats up and cools off much quicker than the ocean, and there is a noticeable difference between the darkness of land and ocean, it looks like the picture was taken early in the morning. The sun has not yet had time to warm the land up.

d. On map

e. There are high clouds over the Midwest United States during the time that this photograph was taken. Because the prevailing winds are from the west to the east, this means that the East Coast should expect high clouds in the next couple of days.