This is all that is provided: a) Use the equation for p(z) for a constant densit

Question

This is all that is provided:

a) Use the equation for p(z) for a constant density atmosphere to calculate the approximate height of the 1000, 850, and 500 hPa levels, assuming that the density throughout the troposphere is the same as that at the surface (computed from T0 and P0).

b) Repeat your calculation using the somewhat more accurate expression for p(z) in an isothermal atmosphere assuming that the temperature of the entire atmosphere equals T0 as given above.

c) Finally, repeat your calculation using the most accurate expression for p(z), which in this case is the one for a constant lapse rate atmosphere.

d) For each of the pressure levels given, calculate the error (approximate minus true value) in meters that results from using the simpler constant density and isothermal approximations.

Explanation / Answer

a)   p(z) = ps exp(- Z/H)

       where H = R T0 / g

              Z = H ln (ps/ p)

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