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Turbulent mixing near the ground for the nested grid model
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    The physical principles that have been used to develop mixed-layer models for a surface layer of variable depth "h", are applied instead directly to the bottom layers of-the Nested Grid Model (NGM). This eliminates the need to predict h explicitly and greatly simplifies the application of these ideas. The principles are reviewed in section 2. Generation of turbulence by shear at the top of the mixed region is ignored in this first formulation. In section 3 the principles are expressed as integrals with respect to the sigma coordinate of the NGM, and the NGM history variables of potential temperature and specific humidity are related to the "buoyancy". Section 4 spells out the details of the numerical method as applied to the discrete sigma layers of the model. The numerical method determines how many layers (K) participate in the mixing for each column. It then produces a uniform (larger) value of buoyancy in layers 1 through (K-i), and determines the appropriate decrease in the buoyancy of the capping layer K. Section 5 shows how the changes in buoyancy derived in section 4 can be re-converted to changes in the NGM variables of potential temperature and specific humidity. An entrainment factor xm that describes the mixing between layers K-1 and K is used to effect this conversion. Section 6 describes how the mixing between layers K and K-1 could be modified when saturation occurs in layer K-1. Tests with the Nested Grid Model in winter of 1985-6 were made in which only mechanical stirring was effective over land, because the model did not contain sensible heat flux over land, nor radiation. The stirring increased the horizontal averaged temperature in the bottom layer of the model over land by about 1 deg/day. Changes as large as 10 deg/day were observed in regions of strong wind and stable air. The Appendix contains test results from computations with a single column using fixed values of surface heat flux and mechanical stirring. The functional dependence of the mixed layer depth with time agrees with well-known results from models that are formulated with an explicit mixed layer depth "h".

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