Chapter 2: Problem 6

How might the relative humidity of a parcel of air change as it moves up the side of a mountain? Why?

Short Answer

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Answer: As a parcel of air moves up the side of a mountain, it undergoes adiabatic cooling, resulting in a temperature decrease. This temperature decrease reduces the maximum possible water vapor content in the air, increasing the relative humidity. When the air temperature reaches the dew point, saturation occurs, leading to cloud formation. So, the relative humidity of a parcel of air generally increases as it moves up the side of a mountain.

Step by step solution

Defining Relative Humidity

Relative humidity is the ratio of the current absolute humidity (the amount of water vapor in the air) to the maximum possible absolute humidity (the maximum amount of water vapor the air can hold at a given temperature). Mathematically, it is expressed as: Relative Humidity (RH) = \(\frac{Actual\ Water\ Vapor\ Content}{Maximum\ Possible\ Water\ Vapor\ Content}\) x 100%

Temperature Profile and Adiabatic Process

As a parcel of air moves up the side of a mountain, it undergoes an adiabatic process. An adiabatic process is one in which there is no exchange of heat with the surroundings, which means that the parcel's temperature can only change due to expansion or compression. In our case, as the parcel moves upward, it experiences a decrease in atmospheric pressure, causing it to expand and cool. This is known as the adiabatic cooling process. Temperature decreases with altitude at an approximate rate of 9.8°C/km. This is called the dry adiabatic lapse rate.

Dew Point and Saturation

Dew point is the temperature at which air becomes saturated with water vapor, and any further decrease in temperature will cause the water vapor to condense into liquid water. As the parcel of air cools during the upward movement, the dew point will be reached at some point, causing saturation. When this occurs, microscopic water droplets or ice crystals form, which can lead to cloud formation. The difference between the air temperature and the dew point temperature indicates the degree of saturation.

Relationship between Relative Humidity and Air Temperature

As the air temperature decreases during adiabatic cooling, the maximum possible water vapor content also decreases. However, the actual water vapor content may remain constant, or even increase, if the air parcel moves over a moist surface (such as a body of water). With a decrease in air temperature and a constant or increasing water vapor content, the relative humidity will increase.

Conclusion

As a parcel of air moves up the side of a mountain, it undergoes adiabatic cooling, resulting in a temperature decrease. This temperature decrease reduces the maximum possible water vapor content in the air, increasing the relative humidity. When the air temperature reaches the dew point, saturation occurs, leading to cloud formation. So, the relative humidity of a parcel of air generally increases as it moves up the side of a mountain.

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How might the relative humidity of a parcel of air change as it moves up the side of a mountain? Why?

Short Answer

Step by step solution

Defining Relative Humidity

Temperature Profile and Adiabatic Process

Dew Point and Saturation

Relationship between Relative Humidity and Air Temperature

Conclusion

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