Assume that a parcel of air is forcd to rise up and over a 6000 foot high mountain.The initial temp of the parcel at sea level is 76.5 F, and the LCL of the parcel is 3000 feet. The DAR is 5.5 * F/1000m and the SAR is 3.3*c/1000m. Assume that condensation begins at 100% relative humidity and that no evaporation takes place as the parcel descends.Indicate calculated temperatures to one decimal place.
To calculate the temperature of the parcel of air as it rises and descends over the mountain, we can use the following steps:
1. Calculate the temperature at the lifting condensation level (LCL):
- The initial temperature at sea level is given as 76.5°F.
- The LCL of the parcel is given as 3000 feet.
- The Dry Adiabatic Rate (DAR) is given as 5.5°F/1000 feet.
- To calculate the temperature at LCL, we can use the formula:
LCL Temperature = Initial Temperature - (LCL Height / 1000) * DAR
LCL Temperature = 76.5°F - (3000 / 1000) * 5.5°F/1000 feet
LCL Temperature = 76.5°F - 16.5°F
LCL Temperature = 60°F
2. Calculate the temperature at the peak of the mountain (6000 feet):
- Since the parcel is forced to rise, it will cool at the DRY Adiabatic Rate (DAR).
- To calculate the temperature at the peak, we can use the formula:
Peak Temperature = LCL Temperature - (Peak Height - LCL Height) * DAR
Peak Temperature = 60°F - (6000 - 3000) * 5.5°F/1000 feet
Peak Temperature = 60°F - 15.5°F
Peak Temperature = 44.5°F
3. Calculate the temperature as the parcel descends:
- The Saturated Adiabatic Rate (SAR) is given as 3.3°C/1000 meters.
- Since the parcel is descending, it will warm at the SATURATED Adiabatic Rate (SAR).
- To calculate the temperature as it descends, we can use the formula:
Descent Temperature = Peak Temperature + (Peak Height - LCL Height) * SAR
Descent Temperature = 44.5°F + (6000 - 3000) * 3.3°C/1000 meters
Descent Temperature = 44.5°F + 9.9°F
Descent Temperature = 54.4°F
Therefore, the calculated temperatures are:
- Lifting Condensation Level (LCL) temperature: 60°F
- Peak temperature at 6000 feet: 44.5°F
- Descending temperature after crossing the mountain: 54.4°F
To determine the temperature of the parcel at various altitudes during its ascent and descent over the mountain, we can follow these steps:
Step 1: Calculate the temperature at the lifting condensation level (LCL):
- LCL temperature = initial temperature - (LCL altitude / 1000) * DAR
- LCL temperature = 76.5°F - (3000 ft / 1000) * 5.5°F/1000 ft
- LCL temperature = 76.5°F - 16.5°F
- LCL temperature = 60.0°F
Step 2: Calculate the temperature at the summit of the mountain:
- Summit temperature = LCL temperature - (summit altitude - LCL altitude) * SAR
- Summit temperature = 60.0°F - (6000 ft - 3000 ft) * 3.3°C / 1000 ft
- Summit temperature = 60.0°F - 9.9°C
- Summit temperature = 50.1°F
Step 3: Calculate the temperature at sea level after descending:
- Sea level temperature = Summit temperature + (summit altitude / 1000) * DAR
- Sea level temperature = 50.1°F + (6000 ft / 1000) * 5.5°F/1000 ft
- Sea level temperature = 50.1°F + 33.0°F
- Sea level temperature = 83.1°F
Therefore, the calculated temperatures at each step are:
- Lifting condensation level (LCL): 60.0°F
- Summit temperature: 50.1°F
- Sea level after descending: 83.1°F