Adiabatic Process: Trace The Path Of A Hypothetical Parcel ✓ Solved

Adiabatic Process Trace the Path Of A Hypothetical Parcel As

Adiabatic Process Trace the path of a hypothetical parcel as it moves over a mountain. You will assume the mountain base to be at sea level on both sides with a peak of 3,000 meters (m) and that the initial parcel conditions include a temperature of 10 °Celsius and a lifting condensation level (LCL) of 1,000 m. Be sure to provide a written explanation of all your calculations. Specifically, the following critical elements must be addressed: Calculate parcel temperatures for all windward and lee-side levels and explain your calculations. What would happen to the parcel (size, Ta, relative humidity [RH]), and how would it change as it ascends the windward side and descends the lee side? What would the parcel temperature be at 1,000 m on the windward side, at the peak, 1,000 m on the lee side, and at the lee base? Why would the temperatures be different at the same levels on each side of the mountain? Your assignment must be submitted as a one-page Word document, with double spacing, 12-point Times New Roman font, one-inch margins, and all sources used cited in APA format.

Paper For Above Instructions

Understanding the behavior of an air parcel moving over a mountain is essential in meteorology, particularly in the study of adiabatic processes. This paper outlines the changes in temperature, size, and relative humidity (RH) of a hypothetical air parcel as it ascends the windward side of a mountain, reaches its peak, and descends the lee side, with specific calculations and explanations provided.

Initial Conditions

The initial conditions of the air parcel include a temperature of 10 °C and a lifting condensation level (LCL) of 1,000 m. As the parcel ascends, it cools at the moist adiabatic lapse rate until it reaches its LCL, which is where condensation occurs and cloud formation begins. The moist adiabatic lapse rate typically ranges from 5 to 6 °C per 1,000 m ascent. For this analysis, we will use a value of 6 °C per 1,000 m.

Calculating Temperatures on the Windward Side

1. At LCL (1,000 m):

Using the moist adiabatic lapse rate, we can calculate the temperature change from the initial altitude of sea level (0 m) to the LCL (1,000 m).

• Temperature at LCL (1,000 m) = Initial Temperature - (Lapse Rate × Height)
• Temperature at 1,000 m = 10 °C - (6 °C/1,000 m × 1,000 m) = 4 °C

2. At the Peak (3,000 m):

From the LCL to the peak:

• Temperature at Peak (3,000 m) = Temperature at LCL - (Lapse Rate × Height to Peak)
• Height to Peak = 3,000 m - 1,000 m = 2,000 m
• Temperature at 3,000 m = 4 °C - (6 °C/1,000 m × 2,000 m) = -8 °C

Calculating Temperatures on the Lee Side

As the air parcel starts descending, it warms at the dry adiabatic lapse rate, approximately 10 °C per 1,000 m.

1. At 1,000 m on the Lee Side:

• Temperature at 1,000 m (lee side) = Temperature at Peak + (Lapse Rate × Height Descent)
• Height Descent = 3,000 m - 1,000 m = 2,000 m
• Temperature at 1,000 m (lee side) = -8 °C + (10 °C/1,000 m × 2,000 m) = 12 °C

2. At Lee Base (0 m):

• Temperature at Lee Base = Temperature at 1,000 m (lee side) + (Lapse Rate × Height Descent)
• Height Descent = 1,000 m - 0 m = 1,000 m
• Temperature at Lee Base = 12 °C + (10 °C/1,000 m × 1,000 m) = 22 °C

Changes in Parcel Size and RH

As the parcel ascends the windward side of the mountain, its size increases due to expansion as the pressure decreases with altitude. The temperature decrease leads to an increase in relative humidity until saturation is reached at the LCL, where condensation starts and clouds form. This process reduces the parcel's size due to the loss of water vapor as precipitation occurs.

Descending on the lee side, the parcel warms and can hold more moisture, leading to a decrease in relative humidity. Consequently, the parcel experiences evaporation, resulting in a further reduction in size as it reaches the base of the mountain.

Understanding Temperature Differences

The temperature differences at the same elevations on either side of the mountain can be attributed to the processes of adiabatic cooling and warming. As air ascends the windward slope, it cools due to the expansion caused by lower pressure, leading to lower temperatures. The loss of moisture through precipitation further decreases latent heat release, maintaining cool temperatures at the windward side. Conversely, on the lee side, the air descends, warms up due to compression, and achieves higher temperatures. This phenomenon, often referred to as the rain shadow effect, illustrates the stark temperature and moisture differences across mountainous regions.

Conclusion

The transformation of a hypothetical air parcel as it traverses a mountain highlights key principles of atmospheric behavior, particularly adiabatic processes. The calculations indicate that temperature and humidity levels change significantly based on elevation and the side of the mountain the parcel is on. Understanding these dynamics is crucial for meteorologists in predicting weather patterns and climate variations across diverse landscapes.

References

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