Assume that a parcel of air is forced to rise up and over a 6000-foot-high Sierra Mountain in California (shown above) and descends to the Nevada lee-ward side.

·      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. LCL is the altitude at which the relative humidity of an air parcel will reach 100% with respect to liquid water when it is cooled by dry adiabatic lifting.

·      The DAR is 5.5°F/1000 ft, and the Saturated adiabatic Rate (SAR) is 3.3°F/1000 ft.

·      Calculate the temperature of the parcel at the following elevations as it rises up the windward side of the mountain.

A.  3,000 ft (use dry adiabatic lapse rate of 5.5º F/1,000 ft to find the new temperature) 

°F

B.  6,000 ft (use saturated lapse rate of 3.3º F/1,000 ft to find the new temperature)  

°F

C.  After the parcel of air has descended down the lee side of the mountain to sea level, what is the temperature of the parcel?

°F

(use dry adiabatic lapse rate of 5.5º F/1,000 ft to find the new temperature)  

D.  Where do you think the risk for fire hazard is higher - on the leeward side or windward side of the Sierra Mountain?

Why?  

Answer:

A. The new temperature at 3000 ft is 60^o F

B. The new temperature at 6000 ft is 50.1^o F

C. The temperaure of the parcel at sea level on the leeward side is 83.1^o F.

D.  The risk of fire hazard is higher on the leeward side of the mountain. This is because temperatures are higher on the leeward due to the fact that air warms as it descends the leeward side of the mountain.

Details.

Given;

The elevation of Sierra Nevada = 6000 ft from sea level.

Air temperature at sea level, T = 76.5^o F

L.C.L = 3000 ft

DAR = 5.5^o F/1000 ft

SAR = 3.3^o F/1000 ft

Solution

Note that the air will cool as it rises up the windward side of the mountain at DAR until the L.C.L level is reached. After    L.C.L is reached, the air will cool at SAR.

A.     From sea level to 3000 ft the air cools at DAR.

T = 76.5^o F

Temperature at 3000 ft will be;

T₃₀₀₀ = 76.5^o F— (DAR)*3000

         = 76.5^o F -(5.5/1000)*3000

          = 76.5^o F -16.5^o F

          = 60^o F.

The temperature at 3000 ft is 60^o F.

B.     From 3000 ft to 6000 ft the air will cool at SAL because L.C.L is reached.

       The temperature at 6000 ft will be;

T₆₀₀₀ = 60^o F - (SAR)*(6000-3000)

        = 60^o F -(3.3/1000)*(6000-3000)

         = 60^o F -9.9^o F

          = 50.1^o F.

C.     When the air descends from the top of the mountain to sea level it will warm up at DAR. This is because the air is dry and when it descends it is compressed thus warming.

At the top of the mountain the temperature is 50.1^o F.

At sea level the elevation is 0 ft.

The temperature at sea level is;

T₀ = 50.1^o F + (5.5/1000)*6000

T₀ = 50.1^o F + 33^o F

T_o = 83.1^o F.

D.     The risk of fire hazard is higher on the leeward side of the mountain. This is because temperatures are higher on the leeward due to the fact that air warms as it descends the leeward side of the mountain.