The Influence of Boundary Layer Mixing Strength on the Evolution of a Baroclinic Cyclone

Sub-grid scale turbulence in numerical weather prediction models is typically handled by a PBL parameterization. These schemes attempt to represent turbulent mixing processes occurring below the resolvable scale of the model grid in the vertical direction, and act upon temperature, moisture, and momentum within the boundary layer. This study varies the PBL mixing strength within 4-km WRF simulations of the 26–29 January 2015 snowstorm to assess the sensitivity of baroclinic cyclones to eddy diffusivity intensity. The bulk critical Richardson number for unstable regimes is varied between 0.0–0.25 within the YSU PBL scheme, as a way of directly altering the depth and magnitude of sub-grid scale turbulent mixing. Results suggest varying the bulk critical Richardson number is similar to selecting a different PBL parameterization. Differences in boundary layer moisture availability, arising from reduced entrainment of dry, free tropospheric air, lead to variations in the magnitude of latent heat release above the warm frontal region, producing stronger upper-tropospheric downstream ridging in simulations with less PBL mixing. The more amplified ow pattern impedes the northeastward propagation of the surface cyclone and results in a westward shift of precipitation. Additionally, trajectory analysis indicates ascending parcels in the less-mixing simulations condense more water vapor and terminate at a higher potential temperature level than ascending parcels in the more-mixing simulations, suggesting stronger latent heat release when PBL mixing is reduced. These results suggest spread within ensemble forecast systems may be improved by perturbing PBL mixing parameters that are not well constrained.

Numerical Investigation of Stable Stratification Effects on Wind Resource Assessment in Complex Terrain

In the present study, we perform numerical simulations considering various stable atmospheric conditions for a small-scale simple topography. Based on the obtained simulation results, we visualize the flow field and discuss drastic changes in the flow patterns. A flow pattern similar to the potential flow suddenly appears around an isolated hill as the stability increases, regardless of the inclination angle of the hill. We show that a critical Richardson number clearly exists. Furthermore, the effect of stable stratification on the evaluation of power generation is shown for typical complex terrain. We evaluate the capacity factor (%) of a 2 MW large wind turbine based on one-year virtual mast data and consider the effect of stable stratification. It is shown, in the case of stable stratification, that the capacity factor is 2.775 times greater than that under neutral stratification.

A Second-Order Closure Turbulence Model: New Heat Flux Equations and No Critical Richardson Number

We formulate a new second-order closure turbulence model by employing a recent closure for the pressure–temperature correlation at the equation level. As a result, we obtain new heat flux equations that avoid the long-standing issue of a finite critical Richardson number. The new, structurally simpler model improves on the Mellor–Yamada and Galperin et al. models; a key feature includes enhanced mixing under stable conditions facilitating agreement with observational, experimental, and high-resolution numerical datasets. The model predicts a planetary boundary layer height deeper than predicted by models with low critical Richardson numbers, as demonstrated in single-column model runs of the GISS ModelE general circulation model.

Dependence of the critical Richardson number on the temperature gradient in the mesosphere

Maximum upper atmospheric turbulence results in the mesosphere from convective and/or dynamic instabilities induced by gravity waves. For the first time, by comparing the vertical accelerations induced by wind shear and the buoyancy force, it is shown that the critical Richardson number Ric can be estimated. Dynamic instability is developed for Ri

Analysis of mixed convection past a heated sphere

The hydrodynamic and thermal characteristics for laminar axisymmetric mixed convection from a heated sphere are analyzed numerically in this work. The governing transport equations of conservation of mass, momentum, and energy have been solved using a higher order compact scheme. The results are presented in terms of the distribution of the streamlines, isotherms, and vorticity contours, and local Nusselt number along the sphere surface together with drag coefficient and average Nusselt number. We identify critical Richardson number above which separation of flow is suppressed. It is revealed that the drag coefficient decreases with an increase in the Reynolds number (Re) and the decrease is more profound for lower range of Re. It is further revealed that the drag coefficient increases monotonically with an increase in the Richardson number, while the same decreases with the increase in the Prandtl number. The average Nusselt number increases monotonically with the increase in Reynolds number, Prandtl number, and Richardson number.

Representing Richardson Number Hysteresis in the NWP Boundary Layer

Turbulence in the planetary boundary layer (PBL) transports heat, momentum, and moisture in eddies that are not resolvable by current NWP systems. Numerical models typically parameterize this process using vertical diffusion operators whose coefficients depend on the intensity of the expected turbulence. The PBL scheme employed in this study uses a one-and-a-half-order closure based on a predictive equation for the turbulent kinetic energy (TKE). For a stably stratified fluid, the growth and decay of TKE is largely controlled by the dynamic stability of the flow as represented by the Richardson number. Although the existence of a critical Richardson number that uniquely separates turbulent and laminar regimes is predicted by linear theory and perturbation analysis, observational evidence and total energy arguments suggest that its value is highly uncertain. This can be explained in part by the apparent presence of turbulence regime-dependent critical values, a property known as Richardson number hysteresis. In this study, a parameterization of Richardson number hysteresis is proposed. The impact of including this effect is evaluated in systems of increasing complexity: a single-column model, a forecast case study, and a full assimilation cycle. It is shown that accounting for a hysteretic loop in the TKE equation improves guidance for a canonical freezing rain event by reducing the diffusive elimination of the warm nose aloft, thus improving the model’s representation of PBL profiles. Systematic enhancements in predictive skill further suggest that representing Richardson number hysteresis in PBL schemes using higher-order closures has the potential to yield important and physically relevant improvements in guidance quality.