NWP | Derivation of Turbulent Kinetic Energy (TKE) from YSU/SH

NWP | Eddy Dissipation Rate (EDR)
MPAS | Eddy dissipation rate (EDR)
- We developed a method to estimate the eddy dissipation rate (EDR) using the resolved wind field of the MPAS simulations. (3D field)
- EDR at the altitude of 10km

Turbulent Kinetic Energy

Derivation of TKE from YSU

Shin, H. H., S. Hong, Y. Noh, and J. Dudhia, 2013: Derivation of Turbulent Kinetic Energy from a First-Order Nonlocal Planetary Boundary Layer Parameterization. J. Atmos. Sci., 70, 1795–1805, https://doi.org/10.1175/JAS-D-12-0150.1.

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.

A parameterization for TKE equation is developed to calculate TKE based on meteorological profiles of wind, temperature, and moisture from the YSU PBL model. For this purpose, buoyancy- and shear-generation terms are formulated by the combination of local, nonlocal, and explicit entrainment fluxes, consistent with the YSU scheme. The vertical transport term is also formulated in a similar fashion. To calculate dissipation length scale and parameterize dissipation, a master length scale consistent with the K profile is introduced. Note that this development is for convective boundary layers.
The introduced TKE calculationis a one-way method such that calculated TKE is sensitive to the length scale,given the same mean meteorological fields.
Note that in the TKE budget profiles, the TKE budgets at the lower boundary are excluded. This is because TKE is directly imposed by the lower boundary condition, rather than calculated by solving the TKE equation. Therefore, the underestimated near-surface TKE cannot be inferred from the TKE budgets.

Remarks:

A convective boundary layer is the part of the lower atmosphere that becomes turbulent and well mixed because the surface heats the air from below, making warmer air rise and cooler air sink.
No — not in the sense the paper defines it. The TKE in this study is a boundary-layer diagnostic built for convective boundary layers, so it is meant for the mixed layer and upper part of the PBL, not for free-atmospheric levels like 850 hPa or 10 km.
- The paper’s formulation is based on YSU PBL physics, which parameterizes turbulence within the planetary boundary layer, not the deep free atmosphere.
- The authors explicitly say the development is for convective boundary layers, and their tests are the GABLS2 boundary-layer case, whose top is around 1 km, not 10 km.
- They also note that the lowest boundary TKE is imposed rather than prognosed, so the scheme is not designed as a general atmospheric TKE field.

WRF github

https://github.com/NCAR/MMM-physics/blob/main/bl_shinhong.F90

For first level, it is specific,

Note that in the TKE budget profiles, the TKE budgets at the lower boundary are excluded. This is because TKE is directly imposed by the lower boundary condition, rather than calculated by solving the TKE equation. Therefore, the underestimated near-surface TKE cannot be inferred from the TKE budgets.

This is because TKE is directly imposed by the lower boundary condition, rather than calculated by solving the TKE equation.

   real(kind=kind_phys),     dimension( kts:kte )                            , &
             intent(inout)   ::                                            q2

   real(kind=kind_phys),parameter :: epsq2l = 0.01,c0 = 0.55,ceps = 16.6,g =9.81

   rc02=2.0/(c0*c0)

!
!  lower boundary condition for q2
!
   q2(kts)=max(rc02*ustar*ustar,epsq2l)