Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

Effective Diahaline Diffusivities in Estuaries

<p>The present study aims to estimate effective diahaline turbulent salinity fluxes and diffusivities in numerical model simulations of estuarine scenarios. The underlying method is based on a quantification of salinity mixing per salinity class, which is shown to be twice the turbulent salinity transport across the respective isohaline. Using this relation, the recently derived universal law of estuarine mixing, predicting that average mixing per salinity class is twice the respective salinity times the river run‐off, can be directly derived. The turbulent salinity transport is accurately decomposed into physical (due to the turbulence closure) and numerical (due to truncation errors of the salinity advection scheme) contributions. The effective diahaline diffusivity representative for a salinity class and an estuarine region results as the ratio of the diahaline turbulent salinity transport and the respective (negative) salinity gradient, both integrated over the isohaline area in that region and averaged over a specified period. With this approach, the physical (or numerical) diffusivities are calculated as half of the product of physical (or numerical) mixing and the isohaline volume, divided by the square of the isohaline area. The method for accurately calculating physical and numerical diahaline diffusivities is tested and demonstrated for a three‐dimensional idealized exponential estuary. As a major product of this study, maps of the spatial distribution of the effective diahaline diffusivities are shown for the model estuary.</p>

Large-Eddy Simulations of Stability-Varying Atmospheric Boundary Layer Flow over Isolated Buildings

This study explores the response of flow around isolated cuboid buildings to variations in the incoming turbulence arising from changes in atmospheric boundary layer (ABL) stability using a building-resolving large-eddy simulation (LES) technique with explicit representation of building effects through an immersed body force method. An extensive suite of LES for a neutral ABL with different model resolution and advection scheme configurations reveals that at least 6, 12, and 24 grid points per building side are required in order to resolve building-induced vortex shedding, mean-flow features, and turbulence statistics, respectively, with an advection scheme of a minimum of third-order. Using model resolutions that meet this requirement, 21 building-resolving simulations are performed under varying atmospheric stability conditions, from weakly stable to convective ABLs, and for different building sizes (H), resulting in LABL/H ≈ 0.1 – 10, where LABL is the integral length scale of the incoming ABL turbulence. The building-induced flow features observed in the canonical neutral ABL simulation, e.g., the upstream horseshoe vortex and the downstream arch vortex, gradually weaken with increasing surface-driven convective instability due to the enhancement of background turbulent mixing. As a result, two local turbulence kinetic energy peaks on the lateral side of the building in non-convective cases are merged into a single peak in strong convective cases. By considering the ABL turbulence scale and building size altogether, it is shown that the building impact decreases with increasing LABL/H, as coherent turbulent structures in the ABL become more dominant over a building-induced flow response for LABL/H > 1.

Assessment of global wave models on regular and unstructured grids using the Unresolved Obstacles Source Term

The Unresolved Obstacles Source Term (UOST) is a general methodology for parameterizing the dissipative effects of subscale islands, cliffs, and other unresolved features in ocean wave models. Since it separates the dissipation from the energy advection scheme, it can be applied to any numerical scheme or any type of mesh. UOST is now part of the official release of WAVEWATCH III, and the freely available package alphaBetaLab automates the estimation of the parameters needed for the obstructed cells. In this contribution, an assessment of global regular and unstructured (triangular) wave models employing UOST is presented. The results in regular meshes show an improvement in model skill, both in terms of spectrum and of integrated parameters, thanks to the UOST modulation of the dissipation with wave direction, and to considering the cell geometry. The improvement is clear in wide areas characterized by the presence of islands, like the whole central-western Pacific Basin. In unstructured meshes, the use of UOST removes the need of high resolution in proximity of all small features, leading to (a) a simplification in the development process of large scale and global meshes, and (b) a significant decrease of the computational demand of accurate large-scale models.

A statistical approach to fast nowcasting of lightning potential fields

Thunderstorms and associated hazards like lightning can pose a serious threat to people outside and infrastructure. Thus, very short-term prediction capabilities (called nowcasting) have been developed to capture this threat and aid in decision-making on when to bring people inside for safety reasons. The atmospheric research and operational communities have been developing and using nowcasting methods for decades, but most methods do not rely on formal statistical approaches. A novel and fast statistical approach to nowcasting of lightning threats is presented here that builds upon an integro-difference modeling framework. Inspiration from the heat equation is used to define a redistribution kernel, and a simple linear advection scheme is shown to work well for the lightning prediction example. The model takes only seconds to estimate and nowcast and is competitive with a more complex image deformation approach that is computationally infeasible for very short-term nowcasts.

A Lagrangian Advection Scheme for Solving Cloud Droplet Diffusion Growth

Cloud drop diffusion growth is a fundamental microphysical process in warm clouds. In the present work, a new Lagrangian advection scheme (LAS) is proposed for solving this process. The LAS discretizes cloud drop size distribution (CDSD) with movable bins. Two types of prognostic variable, namely, bin radius and bin width, are included in the LAS. Bin radius is tracked by the well-known cloud drop diffusion growth equation, while bin width is solved by a derived equation. CDSD is then calculated with the information of bin radius, bin width, and prescribed droplet number concentration. The reliability of the new scheme is validated by the reference analytical solutions in a parcel cloud model. Artificial broadening of CDSD, understood as a by-product of numerical diffusion in advection algorithm, is strictly prohibited by the new scheme. The authors further coupled the LAS into a one-and-half dimensional (1.5D) Eulerian cloud model to evaluate its performance. An individual deep cumulus cloud studied in the Cooperative Convective Precipitation Experiment (CCOPE) campaign was simulated with the LAS-coupled 1.5D model and the original 1.5D model. Simulation results of CDSD and microphysical properties were compared with observational data. Improvements, namely, narrower CDSD and accurate reproduction of particle mean diameter, were achieved with the LAS-coupled 1.5D model.