- You are in Bakersfield, CA, which has an elevation of 118 meters above sea level.  You want to know the temperature at the top of Mt. Whitney (Links to an external site.) (elevation 4421 m).  Based on the normal lapse rate, how much colder would you expect the air temperature at the top of the mountain to be?
ÂÂ
- You are in Fresno, CA, which has an elevation of 94 meters above sea level.  You want to know the temperature at the top of Half Dome (Links to an external site.) in Yosemite National Park (elevation 2695 m).  Based on the normal lapse rate, how much colder would you expect the air temperature at the top of Half Dome to be?
The Correct Answer and Explanation is :
To solve both of these problems, we can use the concept of the normal lapse rate, which is the average rate at which temperature decreases with an increase in altitude in the Earth’s atmosphere. The normal lapse rate is generally 6.5°C per kilometer (or 0.0065°C per meter).
1. Temperature difference at the top of Mt. Whitney (from Bakersfield):
- Elevation of Bakersfield: 118 meters
- Elevation of Mt. Whitney: 4421 meters
The temperature difference between these two elevations can be calculated using the lapse rate:
Temperature difference = (Elevation of Mt. Whitney – Elevation of Bakersfield) × Lapse Rate
[
\text{Temperature difference} = (4421 \, \text{m} – 118 \, \text{m}) \times 0.0065 \, \text{°C/m}
]
[
\text{Temperature difference} = 4303 \, \text{m} \times 0.0065 \, \text{°C/m} = 27.95 \, \text{°C}
]
So, based on the normal lapse rate, we would expect the temperature at the top of Mt. Whitney to be 27.95°C colder than in Bakersfield.
2. Temperature difference at the top of Half Dome (from Fresno):
- Elevation of Fresno: 94 meters
- Elevation of Half Dome: 2695 meters
Similarly, we calculate the temperature difference:
[
\text{Temperature difference} = (2695 \, \text{m} – 94 \, \text{m}) \times 0.0065 \, \text{°C/m}
]
[
\text{Temperature difference} = 2601 \, \text{m} \times 0.0065 \, \text{°C/m} = 16.91 \, \text{°C}
]
So, based on the normal lapse rate, we would expect the temperature at the top of Half Dome to be 16.91°C colder than in Fresno.
Explanation:
The normal lapse rate is used to predict how temperature changes with altitude. As you go higher in the atmosphere, the air becomes less dense and holds less heat, causing the temperature to decrease. In both cases, we’re assuming that the air is behaving typically, and that no unusual weather patterns are affecting temperature changes. These results are approximate, as actual temperatures can vary depending on local weather conditions.
In both examples, we calculated the temperature difference by multiplying the elevation difference by the lapse rate, which gives us an estimate of how much cooler the air would be at the higher elevations.