Derivation of turbulent kinetic energy from a first-order nonlocal planetary boundary layer parameterization

Turbulent kinetic energy (TKE) is derived from a first-order planetary boundary layer (PBL) parameterization for convective boundary layers: the nonlocal K-profile Yonsei University (YSU) PBL. A parameterization for the TKE equation is developed to calculate TKE based on meteorological profiles given by the YSU PBL model. For this purpose buoyancy- and shear-generation terms are formulated consistently with the YSU scheme-that is, the combination of local, nonlocal, and explicit entrainment fluxes. The vertical transport term is also formulated in a similar fashion. A length scale consistent with the K profile is suggested for parameterization of dissipation. Single-column model (SCM) simulations are conducted for a period in the second Global Energy and Water Cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS2) intercomparison case. Results from the SCM simulations are compared with large-eddy simulation (LES) results. The daytime evolution of the vertical structure of TKE matches well with mixed-layer development. The TKE profile is shaped like a typical vertical velocity (w) variance, and its maximum is comparable to that from the LES. By varying the dissipation length from 223% to 113% the TKE maximum is changed from about 215% to 17%. After normalization, the change does not exceed the variability among previous studies. The location of TKE maximum is too low without the effects of the nonlocal TKE transport.