A Modification of Turbulent Kinetic Energy Transport in the Convective Boundary Layer of the MYNN Model

Turbulent kinetic energy (TKE) is a key variable in turbulence parameterization schemes. In the Mellor–Yamada–Nakanishi–Niino (MYNN) level-3 and 2.5 models, the turbulent flux of TKE is diagnosed using a downgradient formulation, yet its applicability to buoyancy-dominated convective boundary layers (CBLs) has not been fully assessed. We construct a new large eddy simulation database for a well-developed dry CBL and use it to evaluate the conventional MYNN closure for TKE flux. The results show that the conventional closure fails to correctly diagnose the sign of TKE turbulent flux in the lower part of buoyancy-dominated CBLs. We propose a modified closure that incorporates an additional term capable of representing a counter-gradient TKE flux. We also develop a closure for this new counter-gradient term so that it can be used within the MYNN framework. The modified closure improves the vertical profile of the diagnosed TKE turbulent flux and reduces its overall error by more than 50%.