Measurements from a weather balloon show a temperature of 2 degC at 1500m altitu
ID: 283030 • Letter: M
Question
Measurements from a weather balloon show a temperature of 2 degC at 1500m altitude with
dry air. Measurements at the surface (at sea level) show a temperature of 12 degC, with r =
5(10)-3 g-vapor/g-air. Assuming the properties vary linearly between 0 and 1500m:
a. Calculate the potential temperature for the air as a function of z, between 0 and
1500m (referenced to the surface) and give the value at z = 1000m.
b. Calculate the buoyancy frequency as a function of z and give the value at z = 1000m.
Explanation / Answer
Answer:
In troposphere, the average lapse rate of decreasing temperature with increase in altitude is 6.5 Co.
And the potential temperature is helpful in comparing the temperature at two different altitude, can be calculated as follows;
Pt = T(z)(ps/p) R/Cp
Pt= potential temperature, T(z) = absolute temperature at altitude z, Ps = standard reference pressure (1000 mb), P= absolute pressure, R= gas constant, Cp= specific heat.
And buoyancy frequency can be calculated as follows:
Bf = g/pt* d(pt)/d(z)
Where, Bf = buoyancy frequency, g = acceleration due to gravity, pt = potential temperature, z= altitude