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Hypsometric Equation

Consider the case of a non isothermal atmopshere, where temperature is a function of height, T = T(z), and a layer of atmopshere between z1 and z2, with pressures, p1 and p2 respectively. Integrating the same expression as for an isothermal atmosphere:

This can be integrated in small enough layers that assuming T is constant in each layer is a good approximation. When this is the case, the layer thickness ia proportional to its mean temperature. 

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* All information on this site has come from lecture notes and the associated course text books: 'Atmospheric Science: An introductory survey, 2nd edition, J. M. Hobbs and P. V. Wallace' and 'Meteorology Today: An Introduction to Weather, Climate and the Environment, 10th edition (International), C. D. Ahrens.' Some sections may have been rephrased and altered slightly but all content came from the above mentioned sources unless otherwise stated. 

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