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The square of the standard deviation of the height (p = constant) or of the pressure (h = constant) and the square of the (vector) standard deviation of the wind are found to be approximately linearly related over large areas and through a deep layer extending well into the lower stratosphere. As a result, some statistical characteristics of the large scale motions of the atmosphere depart markedly from those expected on the basis of turbulence theory. An explanation of the empirical relation between the (vector) standard deviation of the wind and the density of the air is offered.

An Approximate Relation between the Variability of Wind and the Variability of Pressure or Height in the Atmosphere