Assume that a parcel of air is forced to rise up and over a 6000-foot high mountain (shown below). 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 the condensation begins at 100% relative humidity and that no evaporation takes place as the parcel descends. Indicate calculated temperatures to one decimal place.
1. Calculate the temp of the parcel at the following elevations as it rises up the windward side of the mountain
A 1000' ________________
B 3000' __________________
C 6000'__________________
2 after the parcel of air has descended dpwn the lee side of the mountain to sea level what is the temperature of the parcel?____________
why?_______________
5.One the winward side of the mountain, should the relative humidity of the parcel change as it rises from 3000 to 6000 feet?__________________
why_____________________
6. As the air rises up the windward side of the mountain
a what is the capacity (saturation mixing rate) of the rising air at 3000 feet?_____________________________g/kg
what is the capacity of the air at 6000 feet?________________________________g/kg
7. what is the capacity of the air after it descended back down to sea level on the lee side of the moutain? ____________
8. Assuming no water vapo is added as the parcel descends down the lee side of the mountain to sea, is the water vapor content (the mixing ration) of the parcel higher or lower than before it began to rise over the mountain?______________________
why_____________________
what is the lifting condensation level of this parcel now? ___________________________feet
1. A 1000' - The temperature of the parcel at 1000 feet would be 74.0 F. (Using the DAR of 5.5 F/1000', the temperature would decrease by 2.5 F because 1000/1000 = 1, and 1 x 5.5 = 5.5, so 76.5 - 5.5 = 71.0 F. The temperature would then increase by 3.0 F because 1000/1000 = 1, and 1 x 3.0 = 3.0, so 71.0 + 3.0 = 74.0 F.)
2. B 3000' - The temperature of the parcel at 3000 feet would be 69.0 F. (Using the DAR of 5.5 F/1000', the temperature would decrease by 16.5 F because 3000/1000 = 3, and 3 x 5.5 = 16.5, so 76.5 - 16.5 = 60.0 F. The temperature would then increase by 3.0 F because 3000/1000 = 3, and 3 x 3.0 = 9.0, so 60.0 + 9.0 = 69.0 F.)
3. C 6000' - The temperature of the parcel at 6000 feet would be 53.0 F. (Using the DAR of 5.5 F/1000', the temperature would decrease by 33.0 F because 6000/1000 = 6, and 6 x 5.5 = 33.0, so 76.5 - 33.0 = 43.5 F. The temperature would then increase by 0 F because the DAR only applies to the first 20,000 feet, so 43.5 + 0 = 43.5 F.)
4. After the parcel of air has descended down the lee side of the mountain to sea level, the temperature of the parcel would be 71.0 F. (Since there is no evaporation taking place as the parcel descends, the temperature remains the same as it was at 1000 feet, which was 71.0 F.)
5. On the windward side of the mountain, the relative humidity of the parcel would not change as it rises from 3000 to 6000 feet. (Relative humidity depends on the moisture content of the air and the air temperature. Since no evaporation or condensation is taking place as the parcel rises, the moisture content remains the same. The temperature changes, but relative humidity does not change without a change in moisture content.)
6. The capacity (saturation mixing rate) of the rising air at 3000 feet would be approximately 8.5 g/kg. (The capacity depends on the temperature. Using the temperature of 74.0 F at 1000 feet, we can calculate the saturation mixing rate using a psychrometric chart or equations.)
The capacity of the air at 6000 feet would be approximately 5.8 g/kg. (Using the temperature of 53.0 F at 6000 feet, we can calculate the saturation mixing rate.)
7. The capacity of the air after it descended back down to sea level on the lee side of the mountain would be approximately 8.5 g/kg. (Assuming no evaporation or condensation occurs, the capacity remains the same as it was at 3000 feet.)
8. Assuming no water vapor is added as the parcel descends down the lee side of the mountain to sea level, the water vapor content (the mixing ratio) of the parcel would be lower than before it began to rise over the mountain. (Since no evaporation or condensation occurs, the amount of water vapor in the parcel remains constant, while the air density increases as the parcel descends, leading to a decrease in the mixing ratio.)
The lifting condensation level of this parcel now would still be the same as it was initially at 3000 feet, since the condensation level is determined by the initial temperature and moisture content at sea level.
To calculate the temperatures at different elevations as the parcel of air rises up the windward side of the mountain, we can use the Dry Adiabatic Rate (DAR) to calculate the temperature change per 1000 feet.
1. Calculate the temperature of the parcel at the following elevations as it rises up the windward side of the mountain:
A. 1000'
To calculate the temperature at 1000 feet, we can use the DAR of 5.5 F/1000':
Initial temperature: 76.5 F
Temperature change at 1000 feet: DAR × (elevation/1000)
Temperature at 1000 feet: 76.5 F + (5.5 F/1000' × 1000/1000) = 82 F
B. 3000'
To calculate the temperature at 3000 feet, we can again use the DAR:
Initial temperature: 82 F
Temperature change at 3000 feet: DAR × (elevation/1000)
Temperature at 3000 feet: 82 F + (5.5 F/1000' × 3000/1000) = 94.5 F
C. 6000'
To calculate the temperature at 6000 feet, we can again use the DAR:
Initial temperature: 94.5 F
Temperature change at 6000 feet: DAR × (elevation/1000)
Temperature at 6000 feet: 94.5 F + (5.5 F/1000' × 6000/1000) = 121.5 F
2. After the parcel of air has descended down the lee side of the mountain to sea level, its temperature will be the same as the initial temperature at sea level, which is 76.5 F. This is because the descending air experiences the Subsiding Adiabatic Rate (SAR) of 3.3 F/1000', which indicates that the temperature does not change during descent.
5. On the windward side of the mountain, the relative humidity of the parcel will change as it rises from 3000 to 6000 feet. As the air rises and cools, it reaches its Dew Point Temperature (DPT) at the Lifting Condensation Level (LCL) of 3000 feet. Beyond the LCL, the air becomes saturated and condensation occurs, releasing latent heat. This latent heat inhibits further cooling, causing the temperature to gradually decrease at a lower rate. Therefore, the relative humidity will decrease as the air rises from 3000 to 6000 feet.
6. a) The capacity (saturation mixing ratio) of the rising air at 3000 feet can be calculated using the temperature. The formula is 7.5 * (e^(0.0621 * temperature / (temperature + 243.5))). Using 94.5 F as the temperature at 3000 feet, we can calculate:
Capacity at 3000 feet: 7.5 * (e^(0.0621 * 94.5 / (94.5 + 243.5))) = 10.3 g/kg
b) Similarly, we can calculate the capacity of the air at 6000 feet using a temperature of 121.5 F:
Capacity at 6000 feet: 7.5 * (e^(0.0621 * 121.5 / (121.5 + 243.5))) = 20.6 g/kg
7. The capacity of the air after it has descended back down to sea level on the lee side of the mountain remains the same as the initial temperature at sea level, which is 76.5 F. The temperature does not change during descent due to the SAR.
8. Assuming no water vapor is added as the parcel descends down the lee side of the mountain to sea level, the water vapor content (mixing ratio) of the parcel will be lower than before it began to rise over the mountain. This is because as the air rises and cools, the saturation mixing ratio decreases due to the decrease in temperature. When the air descends on the lee side of the mountain, it warms up adiabatically and can hold more moisture, resulting in a lower water vapor content.
The lifting condensation level (LCL) of the parcel remains the same as initially stated, which is 3000 feet. The LCL is the elevation at which the air reaches its dew point temperature and condensation begins to occur.
To solve these questions, we need to use the Dry Adiabatic Rate (DAR) and the Saturated Adiabatic Rate (SAR) to calculate temperature changes as the parcel of air rises and descends over the mountain.
1. To calculate the temperature at each elevation on the windward side of the mountain, we can use the DAR. The DAR tells us that the temperature decreases by 5.5°F for every 1000 feet of ascent.
a) At 1000 feet: The parcel is 1000 feet above sea level, so the temperature would be 76.5°F - (1 * 5.5°F) = 71°F.
b) At 3000 feet: The parcel is 3000 feet above sea level, so the temperature would be 76.5°F - (3 * 5.5°F) = 60°F.
c) At 6000 feet: The parcel is 6000 feet above sea level, so the temperature would be 76.5°F - (6 * 5.5°F) = 43.5°F.
2. After the parcel of air has descended down the lee side of the mountain to sea level, the temperature would be the same as the initial temperature at sea level, which is 76.5°F. This is because there is no evaporation or additional cooling/heating as the parcel descends.
5. On the leeward side of the mountain, the relative humidity of the parcel should not change as it descends from 3000 to 6000 feet. The reason is that there is no evaporation or condensation occurring during descent, so the amount of moisture in the air remains constant.
6. The capacity or saturation mixing ratio of the rising air can be calculated using the SAT. At 3000 feet, the capacity is given by the SAR of 3.3°F/1000' = 3.3 * 3 = 9.9 g/kg (grams per kilogram).
At 6000 feet, the capacity remains the same since the relative humidity is already 100% and there is no further condensation. So, the capacity is also 9.9 g/kg.
7. The capacity of the air after descending back down to sea level on the leeward side of the mountain remains the same, at 9.9 g/kg. This is because there is no evaporation or condensation happening during the descent.
8. Assuming no water vapor is added as the parcel descends down the leeward side of the mountain, the water vapor content (mixing ratio) of the parcel would be higher than before it began to rise over the mountain. This is because as the parcel ascends, water vapor condenses and converts into liquid water, reducing the water vapor content.
Answering the final question, the lifting condensation level (LCL) of the parcel is given as 3000 feet. The LCL is the height at which the parcel of air reaches saturation and condensation begins.