Tests of transilient versus flux-gradient turbulence parameterizations for the prediction of surface layer wind profiles

For applications of numerical weather prediction to the wind energy industry, it is critically important to accurately characterize low-level atmospheric wind profiles—not only in the surface layer but in the bulk of the PBL as well. Boundary layer turbulence parameterizations play a critical role in NWP predictions of low-level wind, and most of these parameterizations employ a flux-gradient hypothesis to relate turbulent fluxes to local gradients. Although the flux-gradient relationship is the most widely accepted method of modeling the effects of turbulence, it cannot account for layers of counter-gradient or zero-gradient flux that are common in the CBL. Most of these discrepancies are attributed to the effects of large eddies.

About twenty years ago, a nonlocal turbulence parameterization was developed, which allowed for mixing between nonadjacent model levels, and because of this special property, it was referred to as a transilient model. The transilient turbulence parameterization was effective at reproducing the weak gradients that are found in the interior of the CBL while maintaining strong turbulent fluxes. However, because of its empirical formulation, computational expense, and difficulty in specifying a general form of the matrix of exchange coefficients, it never gained popularity.

In the present study, the transilient concept is resurrected and compared with the Mellor-Yamada Eta and the MRF PBL schemes. All three are tested against large eddy simulations and atmospheric data. The first two PBL schemes were extracted from the NCAR/PSU MM5 code, and the transilient turbulence parameterization used a Richardson number-based criterion to estimate the mixing depth. All three were run in column model form and tested for a number of nocturnal and daytime PBL cases.

Results of the testing revealed that the MRF predicted the upper surface-layer winds rather well in some cases, but its success was due to two compensating errors (overly deep CBL predictions combined with weak surface layer gradients). The Mellor-Yamada closure appeared to best capture the evolution of the boundary layer depth and boundary layer average wind speeds, but the wind speeds in the upper surface layer were slower than in large eddy simulations and atmospheric measurements. Initial tests of the transilient model revealed that it predicted the upper surface layer winds most accurately, but its surface layer gradients were too weak. The parameterization can be tuned to make the surface layer gradients more realistic, but at the expense of entrainment rate predictions. Despite its lack of popularity, the transilient model shows some promise if a general method, based on physically realistic hypotheses, can be developed to calculate the matrix of exchange coefficients.