Assume that a parcel of air is forced to rise up and over a 6000-foot-high mountain (see page 79 in the Laboratory Manual). 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?
1. To calculate the temperature of the parcel at different elevations as it rises up the windward side of the mountain, we need to consider both the Dry Adiabatic Rate (DAR) and the Lifting Condensation Level (LCL).
(a) At 1000 feet, the parcel is still below the LCL of 3000 feet, so it has not reached its saturation point, and condensation has not started. Therefore, we can use the DAR to calculate the temperature change. The DAR is 5.5°F/1000', so for a 1000-foot increase, the temperature decreases by 5.5°F.
Initial temperature: 76.5°F
Temperature change at 1000 feet: -5.5°F
Therefore, the temperature at 1000 feet would be: 76.5°F - 5.5°F = 71.0°F
(b) At 3000 feet, the parcel has reached its LCL. Above the LCL, the temperature decreases at a lower rate known as the Saturated Adiabatic Rate (SAR). In this case, the SAR is given as 3.3°F/1000'.
Temperature change from LCL to 3000 feet: (3000 - 3000) * 3.3°F/1000' = 0°F
Therefore, the temperature at 3000 feet would be the same as at the LCL: 71.0°F
(c) At 6000 feet, we again use the DAR since the parcel is above its LCL. So the temperature change is also 5.5°F/1000'.
Temperature change from 3000 to 6000 feet: (6000 - 3000) * 5.5°F/1000' = 16.5°F
Therefore, the temperature at 6000 feet would be: 71.0°F - 16.5°F = 54.5°F
2.
(a) When the parcel of air descends down the lee side of the mountain to sea level, it compresses adiabatically, which means it gains heat energy. Since no evaporation occurs during its descent, we can assume that the parcel's temperature increases due to compression.
(b) The source of the heat energy is the work done by the descending parcel as it compresses the air molecules in the lower atmosphere. This compression increases the kinetic energy of the air molecules, resulting in a rise in temperature.
3.
(a) On the windward side of the mountain, as the parcel rises from sea level to 3000 feet, the relative humidity of the parcel is decreasing.
(b) The relative humidity decreases because as the parcel rises, it expands and cools at the Dry Adiabatic Rate (DAR). However, there is no moisture added to the parcel, so the actual amount of water vapor remains the same, resulting in a decrease in relative humidity.
4.
(a) On the lee side of the mountain, as the parcel descends from 6000 feet to sea level, the relative humidity of the parcel is increasing.
(b) The relative humidity increases because as the parcel descends, it compresses and warms. The warmer air has a higher capacity to hold moisture, so the amount of water vapor remains constant, but the relative humidity increases due to the decrease in the water vapor's ability to saturate the air.