NLT3D: a non-local three-dimensional turbulence parameterization scheme for next generation numerical weather prediction models
Final Report Abstract
Since grid sizes of numerical weather prediction (NWP) models continuously shrink, parameterization schemes have to be revised for applicability and conceptual problems. Already in the past turbulence schemes have been formulated for non-local vertical transports, i.e., spanning several model layers directly in one timestep to cope with increasing vertical resolution. With horizontal grid sizes entering the range of a few kilometers and below also horizontal turbulence becomes at least partially resolved considering isotropic large eddies filling most of the planetary boundary layer (PBL) depth (∆x ≈ ∆z ≈ hP BL ) in a convective PBL. So, the development of a new non-local three-dimensional turbulence (NLT3D ) scheme has been proposed and executed. The transilient matrix formalism represents a flexible and easily extendable way to formulate non-local three-dimensional turbulent exchange. Provided with both classical K theory for short-range local turbulence and a parameterization based on non-local Richardson numbers for long-range non-local turbulence this formalism represents the physical kernel of the NLT3D scheme. As idealized experiments with a synoptically forced standalone PBL scheme can be problematic due to the missing interaction with the environment, tests with the NLT3D scheme implemented in WRF in an real case setup are performed right from the beginning. First, the NLT3D scheme is classically tested over homogeneously vegetated flat terrain (North-American grass land prairie) during radiation dominated weather periods with weak large scale gradients. The specific cases are taken from the CASES-99 field campaign and WRF simulations (with three nested domains, ∆x=0.05◦ down to 0.005◦ ) are driven by ERA5 reanalyses. For comparison, ACM2 (also a transilient non-local but onedimensional PBL scheme) and MYNN as a classical local scheme are employed. Over homogeneous terrain all three schemes perform similarly well compared to profiles of virtual potential temperature θv , specific moisture qv and horizontal winds vh from 60 radio sondes launched at four different sites. Smaller deviations of the model, which are similar for all three grid sizes, are consistent with slightly too weak surface fluxes (dominated by the models surface and soil scheme) compared to observations. Although all three schemes behave similarly concerning averaged profiles, more significant differences show up when spatial structures, e.g., of horizontal hP BL distributions. This motivates the real case simulation over complex inhomogeneously vegetated terrain as it is found, e.g., in the north-eastern part of the USA. The CAPTEX campaign with a number of chemical, inert tracer releases during different flow patterns represent a well suited data set to capture a more integral turbulence effect. After dispersion and advection of the tracer across the Appalachian mountain range the tracer is observed from an extended array of 84 observation stations on both sides of the mountains. Here, the three PBL schemes behave differently in activity, e.g., in the simulated hP BL and vertical tracer exchange which is much faster with the non-local schemes NLT3D and ACM2 compared to MYNN also simulating the shallowest PBL. In addition, with NLT3D and to a lesser extent also ACM2 the effective transport velocity of the near-surface tracer is much faster and agrees better with the observations than in simulations with MYNN. This can be traced back to an effective upward mixing of the tracer to the upper PBL, where stronger winds prevail, and an ahead downward mixing back to the surface, so that vertical tracer cross sections exhibit structures like breaking water waves. Accelerations due to a stronger downward mixing of momentum only play a minor role here. As statistical analyses with fraction skill scores confirm, the overall tracer transport is most realistically captured by NLT3D. The overall performance of NLT3D is also significantly driven by the inclusion of the horizontal turbulence. This is shown with an artificially one-dimensional version NLT1D (NLT3D with horizontal turbulence effects switched off) the employment of which weakens the above mentioned acceleration of horizontal tracer transport and degrades the statistical FSS results. Summarizing horizontal turbulence and, thus, the three-dimensional parameterization of turbulence plays a surprisingly important role already at grid sizes of a few kilometers, at least in convective PBL regimes. The parameterization non-local vertical transports not only influences the vertical structure of the PBL, but is also beneficial for the realistic simulation of horizontal transports.
Publications
- A nonlocal three-dimensional turbulence parameterization (NLT3D ) for numerical weather prediction models, Quart. J. Roy. Meteor. Soc.
V. Kuell and A. Bott
(See online at https://doi.org/10.1002/qj.4195)
