Dz

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

Figure 6.5 Illustration of the size of a parcel as it is lifted adiabatically. The volume of the spherical parcel was calculated from (3.43).

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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