ATMO 336 - Weather, Climate, and Society - Homework #4

Due in class on Thursday, March 2^nd

Answer the following questions on a separate sheet of paper. DO NOT write answers on this page. If you need to calculate an answer, you must show your work. Tables of saturation mixing ratios for both Fahrenheit and Celsius temperature are provided below. Make sure you read and answer all the parts to each question! Answers for each question may not be weighted equally.

Temperature (ºF)	Sat. Mixing Ratio (g/kg)	Temperature (ºF)	Sat. Mixing Ratio (g/kg)	Temperature (°F)	Sat. Mixing Ratio (g/kg)
10	1.52	40	5.28	70	15.95
15	1.89	45	6.40	75	18.94
20	2.34	50	7.74	80	22.43
25	2.88	55	9.32	85	26.48
30	3.54	60	11.19	90	31.16
35	4.33	65	13.38	95	36.56

Temperature (ºC)	Sat. Mixing Ratio (g/kg)	Temperature (ºC)	Sat. Mixing Ratio (g/kg)	Temperature (ºC)	Sat. Mixing Ratio (g/kg)
-30	0.30	5	5.0	25	20
-20	0.75	10	7.0	30	26.5
-10	2.0	15	10	35	35
0	3.5	20	14	40	47

1. Clouds most often form when air is lifted upward and cools below its dew point temperature, but this is not the only way clouds can form. Clouds can also form when warm, moist air is mixed with cold air. For example, “steam fog” sometimes occurs when cold air moves over a warmer water surface. Suppose a cold wind blows over a warm lake. The temperature and relative humidity are given below for an air parcel just above the lake surface and an air parcel embedded in the cold wind.

Air Parcel above Lake		Air Parcel in Cold Wind
Air Temperature	65° F	Air Temperature	35° F
Relative Humidity	97 %	Relative Humidity	80 %

(a) Compute the mixing ratio for each air parcel. You will need to use the table of saturation mixing ratios in Fahrenheit.

(b) Assume that the parcels mix equally, such that the temperature of the mixed parcels is the average of the two parcel temperatures (i.e., 50° F) and the mixing ratio is the average of the two mixing ratios computed in part (a). Will a fog form? Explain your answer.

2. “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. Don’t worry about mixing parcels in this case. The function of the cold coastal water is to cool the warm, moist air coming from well offshore.

(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.

3. Answer the following questions and fill in tables for each part below. Re-write tables on your own paper. Do not squeeze answers into the tables below. You will need to use the table of saturation mixing ratios provided in Celsius for this problem. You are going to follow a parcel of air that is forced to rise up a mountain, then back down the other side.

(a) Fill in the table below for an air parcel forced to rise from 0 meters up to the top of a 4,000 m mountain. At what altitude, if at all, will a cloud start to form?

Altitude	Parcel Temperature	Parcel Dewpoint Temperature	Saturated?
4,000 m	*	*	*
3,000 m
2,000 m
1,000 m
0m	25º C	5º C	No

(b) Bring the parcel back down the other side of the mountain. If a cloud developed on the way up, assume that the cloud evaporates on the way down. Fill in the table below. Don't worry about stability. (HINT: 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 goes up.)

Altitude	Parcel Temperature	Parcel Dewpoint Temperature	Saturated?
4,000 m	*	*	*
3,000 m
2,000 m
1,000 m
0 m

* these values come from the corresponding entries in the table from Part (a)

(c) Repeat part (b), but this time assume that all the liquid or ice that condensed into a cloud as the parcel went up the mountain fell out of the parcel as precipitation. Fill out the same table as for part (b). Remember: this time there is no cloud to evaporate on the way down.

(d) Compute the relative humidity for each of the parcels at 0 m from parts (a), (b), and (c). If the exact values are not found in the saturation mixing ratio table, you will have to make estimates based on the nearest values. Explain why the parcel in part (c) arrives back on the ground warmer than it was before it went up and over the mountain.

4. Answer the following questions or fill in tables for each part below. Re-write tables on your own paper. Do not squeeze answers into the tables below.

The lifted index (LI) is defined as the difference between the environmental air temperature at 500 mb (T₅₀₀) and the air temperature inside an air parcel after it has been lifted from the surface up to 500 mb (T_Parcel). 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 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 (this is T500)	(this is 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 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.