An analysis of the errors associated with the determination of atmospheric temperature from atmospheric pressure and density data

A graph was developed for relating delta T/T, the relative uncertainty in atmospheric temperature T, to delta p/p, the relative uncertainty in the atmospheric pressure p, for situations, when T is derived from the slope of the pressure-height profile. A similar graph relates delta T/T to delta roh/rho, the relative uncertainty in the atmospheric density rho, for those cases when T is derived from the downward integration of the density-height profile. A comparison of these two graphs shows that for equal uncertainties in the respective basic parameters, p or rho, smaller uncertainties in the derived temperatures are associated with density-height rather than with pressure-height data. The value of delta T/T is seen to depend not only upon delta p or delta rho, and to a small extent upon the value of T or the related scale height H, but also upon the inverse of delta h, the height increment between successive observations of p or rho. In the case of pressure-height data, delta T/T is dominated by 1/delta h for all values of delta h; for density-height data, delta T/T is dominated by delta rho/rho for delta h smaller than about 5 km. In the case of T derived from density-height data, this inverse relationship between delta T/T and delta h applies only for large values of delta h, that is, for delta h 35 km. No limit exists in the fineness of usable height resolution of T which may be derived from densities, while a fine height resolution in pressure-height data leads to temperature with unacceptably large uncertainties.