Finally,
dr |
g | |
dz |
dry adiabat |
CP |
[dry adiabatic lapse rate].
[dry adiabatic lapse rate].
This very simple and elegant result does not depend on the actual temperature profile of the atmosphere. We can evaluate this formula to find:
dr dZ
dry adiabat
Note that the adiabatic lapse rate rd is defined to be a positive number. Figure 6.5 shows the temperature and size of a parcel being lifted adiabatically from the surface to 10 km.
Example 6.5: dry adiabatic atmosphere Consider the pressure profile of an atmosphere whose vertical dependence of temperature is that of a dry adiabat. This
is an atmosphere that is thoroughly mixed in the vertical dimension. (For example, the turbulent boundary layer which occupies the lowest 1 to 2 km of the air column. We will show this later.) Its temperature falls off linearly as dT/dz = -g/cp. For these conditions 6 is the same throughout. Such an atmospheric profile is called isentropic. We have the hydrostatic equation and Poisson's equation dp p
dz RT&
kPo)
We take 6 to be a constant in Poisson's equation. Thus, dp pg pO
Integrating from (p = po, z = 0) to (p = p, z = z):
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