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Second-order turbulence models of the Mellor and Yamada type have been widely used to simulate the planetary boundary layer (PBL). It is, however, known that these models have several deficiencies. For example, assuming the production of the turbulent kinetic energy equals its dissipation, they all predict a critical Richardson number that is about four times smaller than the large eddy simulation (LES) data in stably stratified flows and are unable to distinguish the vertical and lateral components of the turbulent kinetic energy in neutral PBLs, and they predict a boundary layer height lower than expected.
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Cheng et al. (2002) studied this question.
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