Parameterizing the Height of the Stable Atmospheric Boundary Layer

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Abstract
A critical assessment is made of the various diagnostic relations for the height of the nocturnal boundary layer, as well as of their past comparisons with experimental data. The parametric relations involving the characteristics of the whole boundary layer are found to be less satisfactory than those involving only the surface layer variables. The latter are tested against the Cubauw tower data for the selected winter periods when the mixed-layer height h was measured directly with an acoustic sounder. It is found that h has rather poor correlation with the height ho to which the effect of surface cooling extends. Its correlation with hu, the height of the maximum in wind speed, is fair (r ≈ 0.5) during strong stability conditions, but poor in slight to moderate stability conditions. Better correlations (r ≈ 0.7) are obtained with u*/f, (u*L/f)1/2 and Deardorff's (1972b) interpolation formula where u* is the friction velocity, L is the Obukhov length and f the Coriolis parameter. The parametric relations based on the linear regression of h with the above height parameters are given. These may be used in the absence of direct measurements of h, especially when the type of information required for using a more accurate prognostic rate equation is not available.

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