Assume that a parcel of air is forced to rise up and over a 6000-foot-high mountain. The initial temperature of the parcel at sea level is 76.5°F, and the lifting condensation level (LCL) of the parcel is 3000 feet. The DAR is 5.5°F/1000’ and the SAR is 3.3°F/1000’. Assume that condensation begins at 100% relative humidity and that no evaporation takes place as the parcel descends. Indicate calculated temperatures to one decimal point.
1. Calculate the temperature of the parcel at the following elevations as it rises up the windward side of the mountain:
(a) 1000’_______°F
(b) 3000’ ______ °F
(c) 6000’ ______ °F
2. (a) After the parcel of air has descended down the lee side of the mountain to sea level, what is the temperature of the parcel?
________________________ °F
(b) Why is the parcel now warmer than it was at sea level on the windward side (what is the source of the heat energy)?
3. (a) On the windward side of the mountain, is the relative humidity of the parcel increasing or decreasing as it rises from sea level to 3000 feet?
(b) Why?
4. (a) On the lee side of the mountain, is the relative humidity of the parcel increasing or decreasing as it descends from 6000 feet to sea level?
(b) Why?
To calculate the temperature of the parcel at different elevations as it rises up the windward side of the mountain, we need to understand the lapse rates and the process of condensation.
1a. To calculate the temperature at 1000 feet, we can use the Dry Adiabatic Rate (DAR) which is 5.5°F/1000’. Since the initial temperature at sea level is 76.5°F, we can use the following formula to calculate the temperature at 1000 feet:
T = TI - (DAR x h)
Where:
T = Temperature at 1000'
TI = Initial Temperature at sea level (76.5°F)
DAR = Dry Adiabatic Rate (5.5°F/1000')
h = Change in altitude (1000 feet)
Substituting the values into the formula:
T = 76.5 - (5.5 x 1)
T = 76.5 - 5.5
T = 71.0°F
Therefore, the temperature of the parcel at 1000 feet is 71.0°F.
1b. To calculate the temperature at 3000 feet, we can use the Lifting Condensation Level (LCL) at 3000 feet. The LCL marks the altitude at which the parcel reaches 100% relative humidity and condensation begins. At this point, the temperature remains constant. Therefore, the temperature at 3000 feet is the same as the temperature at the LCL.
From the given information, the LCL is at 3000 feet, so the temperature at 3000 feet is 71.0°F.
1c. To calculate the temperature at 6000 feet, we can use the Saturated Adiabatic Rate (SAR) which is 3.3°F/1000’. Starting from the LCL, the temperature decreases at SAR as the parcel continues to rise.
Using the formula mentioned earlier:
T = TI - (SAR x h)
Substituting the values into the formula:
T = 71.0 - (3.3 x 3)
T = 71.0 - 9.9
T = 61.1°F
Therefore, the temperature of the parcel at 6000 feet is 61.1°F.
2a. After the parcel of air descends down the lee side of the mountain to sea level, the temperature depends on the process of adiabatic compression. As the air descends, it experiences compression and undergoes warming at the Dry Adiabatic Rate (DAR).
Using the formula mentioned earlier:
T = TI + (DAR x h)
Substituting the values into the formula:
T = 61.1 + (5.5 x 6)
T = 61.1 + 33.0
T = 94.1°F
Therefore, the temperature of the parcel at sea level on the lee side is 94.1°F.
2b. The parcel is now warmer than it was at sea level on the windward side because of adiabatic compression during descent. As the parcel descends, it is compressed and its air molecules become more closely packed together. This compression increases the kinetic energy and temperature of the parcel due to the conservation of energy. The source of heat energy is the conversion of potential energy to kinetic energy during descent.
3a. On the windward side of the mountain, the relative humidity of the parcel is increasing as it rises from sea level to 3000 feet. This is because as the parcel rises, it cools due to the adiabatic expansion and the decrease in temperature with height. As the temperature drops, the air reaches its dew point and condensation begins, increasing the amount of moisture in the parcel and therefore increasing the relative humidity.
3b. The relative humidity is increasing because as the parcel rises, it cools and reaches its dew point, resulting in the formation of clouds and eventual precipitation. This increases the amount of moisture present in the air, causing the relative humidity to rise.
4a. On the lee side of the mountain, the relative humidity of the parcel is decreasing as it descends from 6000 feet to sea level. This is because as the parcel descends, it undergoes adiabatic compression, which increases temperature. As the temperature rises, the air can hold more moisture, leading to a decrease in relative humidity.
4b. The relative humidity is decreasing because as the parcel descends and undergoes adiabatic compression, the increase in temperature causes the air to become relatively drier. The increased temperature allows the air to hold more moisture, resulting in a decrease in relative humidity.