Matching in the Convective Planetary Boundary Layer

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Abstract
Monin-Obukhov scaling and convective scaling both apply over a range of heights z given approximately by −L<zzi where L is the Monin-Obukhov length and zi the height of the lowest inversion. This region is defined here as the “convective matching layer”. From the matching conditions, special relations are derived between turbulence statistics, heat flux and height which turn out to be the same as relations previously derived by dimensional analysis in the “free-convection layer”. Thus the convective matching layer is the free-convection layer viewed from a different vantage point. Expressions for the spectra of vertical velocity and temperature can be derived from matching conditions and the hypothesis that they consist of products of two functions, one of which describes the magnitude, the other the shape of the spectra.

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