The Influence of WENO Schemes on Large-Eddy Simulations of a Neutral Atmospheric Boundary Layer

This work explores the influence of Weighted Essentially Non-Oscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage, but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other "Terra Incognita" problems.

An Investigation of the Grid Sensitivity in Large-Eddy Simulations of the Stable Boundary Layer

We revisit the longstanding problem of grid sensitivity, i.e., the lack of grid convergence in large-eddy simulations (LES) of the stable boundary layer. We use a comprehensive set of LES of the well-known Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study 1 (GABLS1) case with varying grid spacings between 12.5 m and 1 m to investigate several physical processes and numerical features that are possible causes of grid sensitivity. Our results demonstrate that there are two resolution regimes in which grid sensitivity manifests differently. We find that changing the numerical advection schemes and the subgrid-scale models alters the simulation results, but the options tested do not fully address the grid-sensitivity issue. Moreover, sensitivity runs suggest that the surface boundary condition and the interaction of the surface with the near-surface flow, as well as the mixing with the free atmosphere, are unlikely to be the causes of the observed grid sensitivity. One interesting finding is that the grid sensitivity in the fine grid-spacing regime (grid spacings $$\le 2\,\mathrm{m}$$ ≤ 2 m ) is closely related to the reduction in the energy content of large-scale turbulence, leading to less turbulence kinetic energy and hence lower boundary-layer heights. The present work demonstrates that there is still an urgent need to address this grid-sensitivity issue in order to perform reliable LES of the stable boundary layer.

Comparison of ice dynamics using full-Stokes and Blatter-Pattynapproximation: application to the central North East Greenland IceStream

Full-Stokes (FS) ice sheet models provide the most sophisticated formulation of ice sheet flow. However, its applicability is often limited due to its high computational demand and its owing numerical challenges. To balance computational demand and accuracy, the so-called Blatter-Pattyn (BP) stress regime is frequently used. Here, we explore the dynamic consequences caused by solving FS and the BP stress regime applied to the central part of the North East Greenland Ice Stream (NEGIS). To ensure a consistent comparison, we use one single ice sheet model to run the simulations under identical numerical conditions. A sensitivity study to grid resolution reveals that velocity differences between the FS and BP solution emerge below ~1 km horizontal resolution and continuously increases with resolution. Generally, BP produces higher surface velocities than FS, at a resolution of 0.1 km up to 5.8 % on average. In an extreme case, estimated ice discharge rates are up to 8 % overestimated by BP; in a rather classical case, BP reveals up to 3 % more ice discharge. Based on these minor model disagreements and given other large uncertainties in ice sheet projections, we conclude that the use of FS seems not an urgent issue and takes a secondary role in narrowing uncertainties of current sea-level projections. However, the englacial advection schemes from both stress regimes indicate severe impacts on internal layers of ice sheets.

On the sensitivity of hurricane intensity and structure to horizontal tracer advection schemes in FV3

We investigate the sensitivity of hurricane intensity and structure to the horizontal tracer advection in the Geophysical Fluid Dynamics Laboratory (GFDL) Finite-Volume Cubed-Sphere Dynamical Core (FV3). We compare two schemes, a monotonic scheme and a less diffusive positive-definite scheme. The positive-definite scheme leads to significant improvement in the intensity prediction relative to the monotonic scheme in a suite of five-day forecasts that mostly consist of rapidly intensifying hurricanes. Notable storm structural differences are present: the radius of maximum wind (RMW) is smaller and eyewall convection occurs farther inside the RMW when the positive-definite scheme is used. Moreover, we find that the horizontal tracer advection scheme affects the eyewall convection location by affecting the moisture distribution in the inner-core region. This study highlights the importance of dynamical core algorithms in hurricane intensity prediction.

A Fast Linear Semi-Lagrangian Advection Scheme Coupled with Spectral (bin) Microphysics to Simulate an Idealized Super Cell Storm in WRF

A new, computationally efficient Semi-Lagrangian advection (SLA) scheme was used to simulate an idealized supercell storm using WRF coupled with Spectral (bin) Microphysics (SBM). SLA was developed to make complicated microphysical schemes more computationally accessible to cloud resolving models. The SLA is a linear combination of Semi-Lagrangian schemes of the first and the second order. It has relatively low numerical diffusion, a high level of mass conservation accuracy, and preserves the sum of multiple advected variables. In addition to idealized tests, comparisons were made with standard WRF higher-order, non-linear advection schemes. Tests of the SLA were performed using different weighting coefficients of γ for the combination of the first and second order components. The results of SLA on grids of 1 km, 500 m, and 250 m agree well with those of the standard WRF advection schemes, with results most similar to simulations with 250 m grid spacing. At the same time, the advection CPU time required by the SLA was 2.2 to 3 times shorter than the WRF advection schemes. The speed-up occurred in part because of the utilization of the same advection matrix for the advection of all hydrometeor mass bins. The findings of this work support the hypothesis that cloud microphysical simulation is more sensitive to the choice of microphysics than to the choice of advection schemes, thereby justifying the use of computationally efficient lower order linear schemes.

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>

New continuity-based velocity interpolation scheme for staggered grids

<p>In the marker-in-cell method combined with staggered finite differences, Lagrangian markers carrying information on material properties are advected with the velocity field interpolated from the staggered Eulerian velocity grid. With existing schemes, velocity interpolation from the grid points to markers violates (to some extent) mass conservation requirement that causes excess convergence/divergence of markers and opening marker gaps after significant amount of advection. This effect is especially well visible in case of diagonal simple shear deformation along planes that are oriented at 45 degrees to the grid and marker circulation through grid corners.</p><p>Here, we present a new second order velocity interpolation scheme that guarantees exact interpolation of normal strain rate components from pressure nodes (i.e. from the locations where these components are defined by solving of the mass conservation equation). This new interpolation scheme is thus applicable to both compressible and incompressible flow and is trivially expendable to 3D and to non-regular staggered grids.</p><p>Performed tests show that, compared to other velocity interpolation approaches, the new scheme has superior performance in preserving continuity of the marker field during the long-term advection including the diagonal simple shear deformation and marker circulation through grid corners. We showcase a performance-oriented implementation of the new scheme using Julia language's shared memory parallelisation features. The Julia implementation of the new advection schemes further augments the ParallelStencil.jl  related application collection with advection routines.</p>