Toward Parameterization of the Stable Boundary Layer

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Abstract
The bulk Richardson number formula for the depth of the nocturnal boundary layer (NBL) is compared to the Wangara observational data. A correlation of 0.89 is found between the observed NBL depth and the depth calculated using a fixed value of bulk Richardson number. This observed NBL depth is defined as the top of a layer, found consistently in the observations, in which the virtual potential temperature varies linearly with height. The Richardson number expression is also found to be a better estimator of NBL depth, defined in a number of other ways. Based on these findings, a simple three-layer parameterization of the NBL is developed and shown to compare favorably with observations. Within the framework of a prognostic equation for virtual potential temperature, the model diagnoses two important NBL heights, one corresponding to the top of the turbulent layer and the other to the inversion or cooling depth. The single prognostic equation, along with four accompanying diagnostic expressions, also describes the temperature structure of the entire NBL. The model is simple enough to be integrated on a programmable hand calculator.

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