NATS 101, Sections 31 and 32

Homework #5

Your homework must be typed. Make sure you read and answer all the parts to each question!

1. “Advection fog” is common along the northern California coast in summer. The main reason that fog forms in this region is that the surface ocean water near the coast is much colder than the surface ocean water farther offshore. When surface winds are westerly, warm, moist air from the Pacific Ocean is carried over the cold, coastal waters, forming fog. This fog is often carried inland by the westerly winds (e.g., San Francisco fog).

(a) Explain why fog forms when the warm, moist air contacts the much colder coastal waters.

(b) Over land, this fog often persists through the morning hours, but “burns off” as the afternoon wears on. This occurs because some sunlight is able to penetrate through the fog and warm the ground. Explain how this would act to dissipate the fog (of course, the fog doesn’t actually “burn”). Would you expect the fog to dissipate from the bottom up or from the top down? Explain.

2. The rain shadow effect. As air is forced to rise up a mountain, clouds may form. Some of the condensed water may then rain out of the clouds on the windward slopes and mountain tops. After the air moves over the mountain top, it is forced to sink back down on the leeward side of the mountain. In this sinking air, any remaining clouds will evaporate as the air warms by compression. At the bottom of the leeward side of the mountain, the air is often warmer and much less humid than it was before it was forced up and over the mountain. Answer the following questions and fill in tables for each part below. Create your own tables (using WORD perhaps). You are going to follow a parcel of air that is forced to rise up a mountain, then sink back down the other side of the mountain.

(a) Fill in the table below for an air parcel forced to rise from 0 meters up to the top of a 6,000 m mountain. At what altitude will a cloud start to form?

Altitude	Parcel Temperature	Parcel Dew point Temperature
6,000 m
5,000 m
4,000 m
3,000 m
2,000 m
1,000 m
0m	20º C	10º C

(b) Bring the parcel back down the other side of the mountain. Initially the parcel contained 7 g of water vapor per kilogram of dry air. This is based on a dew point temperature of 10° C and the table of saturation mixing ratios that was distributed as a class handout. Assume that 59% of the total amount of water in the parcel fell out of the parcel as rain or snow on the mountain. This means that the parcel contains only 3 g of water per kilogram of dry air just before it is forced to come down the other side of the mountain. Fill in the table below for the air parcel being forced to sink from 6,000 m down to 0 m. (HINTS: when parcels move down in the atmosphere, they warm by compression. Unsaturated parcels warm by 10º C for every 1000 m drop in elevation. Parcels that contain clouds warm more slowly because energy is required to evaporate the cloud, therefore a parcel which contains a cloud warms by only 6º C for every 1000 m drop in elevation until the entire cloud evaporates. Keep in mind that as a cloud evaporates, the dew point temperature will change. You will have to determine when the cloud completely evaporates from the parcel. This happens when all of the water is in the form of water vapor. For a mixing ratio of 3 g of water vapor per kilogram of dry air, the air is saturated at a temperature of -2° C. This means that the dew point temperature of the sinking parcel can not become higher than -2° C.

Altitude	Parcel Temperature	Parcel Dew point Temperature
6,000 m	* (from part a)	* (from part a)
5,000 m
4,000 m
3,000 m
2,000 m
1,000 m
0 m

* to get started you need to copy the values you computed at 6000 m from the table in Part (a)

(c) Explain why the parcel in part (b) arrives back on the ground warmer than it was before it went up and over the mountain.

3. Answer the following questions or fill in tables for each part below. Create your own tables (using WORD perhaps).

The lifted index (This is labeled as LI in the equations below) is defined as the difference between the environmental air temperature at 500 mb (This is labeled as T₅₀₀ in the equation below) and the air temperature inside an air parcel after it has been lifted from the surface up to 500 mb (This is labeled as T_Parcel in the equation below). Meteorologists use the lifted index to access the stability of the atmosphere.

LI = T₅₀₀ - T_Parcel

(a) Explain why the atmosphere is said to be stable when the lifted index is positive and unstable when the lifted index is negative.

(b) The following information is available for Asheville, NC (elevation ~500 m above sea level) at 8:00 AM. Fill in the table by lifting an air parcel from the surface up to 5500 m, where air pressure is 500 mb. At what altitude does a cloud start to form? What is the lifted index at 8:00 AM? Is the atmosphere stable or unstable for parcels lifted to 500 mb? Notice that each step up in the table is separated by 1000 m in altitude.

Air Pressure	Altitude (m)	Atmospheric Temperature (°C)	Parcel Temperature (°C)	Parcel Dew Point (°C)
500 mb	5500	-20 (this is T500)	(the value you fill in this box will be TParcel)
----------	4500	-13
----------	3500	-6
----------	2500	1
----------	1500	8
----------	500	10	10	0

(c) Later that day at 3:00 PM, the following conditions were measured in Asheville, NC. Fill in the table below by lifting an air parcel from the surface up to 5500 m, where air pressure is 500 mb. At what altitude does a cloud start to form? What is the lifted index at 3:00 PM? Is the atmosphere stable or unstable for parcels lifted to 500 mb?

Air Pressure	Altitude (m)	Atmospheric Temperature (°C)	Parcel Temperature (°C)	Parcel Dew Point (°C)
500 mb	5500	-20
----------	4500	-13
----------	3500	-5
----------	2500	3
----------	1500	11
----------	500	20	20	0

(d) What change took place in the atmosphere between 8:00 AM and 3:00 PM that caused the stability of the atmosphere to change? Explain why this change tends to make the atmosphere more unstable.

End of homework. There will not be a 4^th question.