Problem 56338. Pressure for a given Above Sea Level Altitude

Meg Noah

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For altitudes up to the stratosphere (around 11 km above mean sea level), the air pressure can be estimated from:
 with 
where the observed surface values are:
static pressure at base of atmosphere (sea level if h0 = 0) in mb
temperatuer at base of atmosphere in K
altitude above the base of atmosphere in m
base of atmosphere (sea level if h0=0) in m
and the constants are:
molar mass of Earth’s air = 0.0289644 [kg/mol]
standard temperature lapse rate [K/m] = -0.0065 [K/m]
Rydberg constant = 8.31432 N m/mol K 
9.80665 m/s^2 is the acceleration due to gravity at the surface of Earth
and for altitudes above the tropopause (the base of the stratosphere) up to about 20,000 m):
 with 
where on average:
 = 11 km
 = 226.32 mb
K
Write a function that returns the pressure in millibars as a function of altitude in meters.  The surface observation variables should be scalars.  Assume the base altitude and surface observations are made at sea level (h0=0).  The input altitude above sea level can be a vector.