Fine Grids and Better Turbulence Schemes Prove Crucial for Simulating Dangerous Mountain Waves

High above the Southern Alps of New Zealand, air streaming over the jagged spine of the mountains sets the atmosphere ringing like a struck bell. These oscillations, known as mountain waves or orographic gravity waves, can climb from the ridgeline into the stratosphere, growing in amplitude as the air thins, and in the worst cases breaking apart into violent pockets of turbulence that no pilot wants to encounter. A new study by Roshny Siri Jagan and Juerg Schmidli of Goethe University Frankfurt, published in Atmospheric Chemistry and Physics, dissects exactly how well modern weather models can capture these waves and their attendant turbulence, and the answer depends in surprising ways on both the fineness of the computational grid and the mathematical machinery used to represent turbulence.

The researchers turned their attention to a well-documented event from the Deep Propagating Gravity Wave Experiment, or DEEPWAVE, a field campaign conducted over New Zealand in 2014. On 12 July of that year, a research aircraft flown by the German Aerospace Center traced a rectangular path across the South Island, sampling the atmosphere at two stacked levels: one near 7.9 kilometers altitude and another near 10.9 kilometers, close to the tropopause. The meteorological setup was favorable for wave generation, with moderate northwesterly winds of roughly 10 to 15 meters per second at 5 kilometers altitude blowing perpendicular to the Southern Alps, and about 20 meters per second near the tropopause, with little change in wind direction with height. Those stacked flight legs provided rare, high-frequency in situ measurements of waves and turbulence signatures near the tropopause, exactly the kind of ground truth that model developers crave.

The simulation tool at the heart of the study is the ICON model, the ICOsahedral Nonhydrostatic modeling framework developed jointly by the German Weather Service and the Max Planck Institute for Meteorology. ICON uses an icosahedral-triangular grid built from geodesic Delaunay triangulation, a height-based vertical coordinate and C-grid staggering of its variables. Jagan and Schmidli ran ICON in numerical weather prediction mode at horizontal grid spacings of approximately 2 kilometers, 1 kilometer and 500 meters, all with 137 vertical levels and a model top at 30 kilometers. They then varied the maximum vertical grid spacing in the upper troposphere and lower stratosphere, the critical region spanning roughly 6 to 25 kilometers altitude, among 400, 200 and 100 meters. To anchor the finest end of the comparison, they added an online-nested large-eddy simulation that zoomed down to a remarkable 130 meters over the southern flight segment, using four nested domains stepping from 1 kilometer down to the 130-meter innermost nest.

The turbulence question was addressed by pitting two schemes against each other. The first is the operational turbulent kinetic energy scheme, which predicts a single TKE value and augments the classical shear-driven turbulence budget with empirical extra source terms, one for large-scale horizontal shear and one for breaking subgrid-scale mountains, both originally designed to support aviation turbulence products such as the eddy dissipation rate. The second is the newly developed two-energy scheme, which carries two prognostic turbulence energies, dynamically adjusts its mixing length, avoids prescribed minimum diffusion coefficients and employs an assumed probability density function method for buoyancy production, all intended to better handle the anisotropic, strongly stratified turbulence found aloft rather than the boundary-layer conditions for which most closures were originally tuned.

The reference simulation, run at 1 kilometer resolution with the two-energy scheme, painted a vivid picture of the event. Alternating bands of ascent and descent stretched downstream of the main ridge from the mid-troposphere into the lower stratosphere, strongest in the troposphere and weakening with height. A powerful wave with vertical velocities exceeding 3 meters per second rose above the Mount Cook region, New Zealand’s highest summit, while a weaker wave formed above the Two Thumb Range farther southeast. The simulated wave field proved quasi-stationary across the three-hour flight window, which made the comparison with the aircraft data meaningful. Against the observations, the model agreed reasonably well on the lower flight leg but underestimated wave amplitude on the upper leg, and the large-eddy simulation better captured the wavelength and phase of the waves even though the coarser NWP runs better reproduced their amplitude.

Resolution emerged as a decisive factor. At 2 kilometers, the simulated waves took on an artificially hydrostatic character, their horizontal wavelengths stretching as the model lost the ability to represent shorter scales. At 500 meters the waves became more non-hydrostatic and vertically aligned, and the number of resolved waves multiplied as shorter wavelengths entered the picture, an effect even more pronounced at 130 meters in the large-eddy simulation, where clear examples of trapped lee waves appeared in the stable layer below about 5 kilometers. Vertical resolution mattered just as much: simulations with 400-meter vertical spacing showed clear differences from the reference, particularly in the stratosphere, while 200-meter and 100-meter runs were nearly identical, indicating that near-convergence of the primary wave requires vertical grid spacing of 200 meters or finer in the upper troposphere and lower stratosphere.

The most striking finding concerned the turbulence schemes themselves. Both produced essentially the same resolved wave structures, yet the parameterized turbulent kinetic energy differed enormously between them. The operational TKE scheme generated substantially higher TKE throughout the wave field, with turbulence patches sprinkled across the troposphere and even reaching into the lower stratosphere, whereas the two-energy scheme sensibly confined turbulence to the atmospheric boundary layer and the strongest low-level wave regions. By systematically switching off the empirical source terms, the researchers traced the excess to the horizontal-shear term. This term is a two-dimensional Smagorinsky-type closure that assumes grid-scale deformation feeds an irreversible cascade into unresolved turbulence, but in the simulated mountain-wave case much of the deformation came from large, coherent, largely reversible gravity waves. Unable to tell the difference, the closure converted wave-related deformation into spurious TKE, which is why the excess energy appeared spatially correlated with the wave field rather than with genuinely turbulent regions.

Further confirmation came from bulk diagnostics averaged over a subdomain of the Southern Alps. Area-averaged vertical velocity variance at 500 meters matched the large-eddy simulation closely in the lower troposphere, while the 1 and 2 kilometer runs systematically underestimated it in the trapped-lee-wave layer. Above that layer, the 1 and 0.5 kilometer runs agreed well, signaling near-convergence for the dominant wave. Notably, the momentum flux profiles at 1 kilometer were nearly identical regardless of turbulence scheme, and the spurious horizontal-shear TKE left no corresponding signature in the wave drag, a decoupling the authors interpret as further evidence that the extra turbulence was artificial. The low-level gravity-wave momentum flux, a key target quantity for gravity-wave drag parameterizations, kept increasing as resolution improved from 1 kilometer to 500 meters, meaning the bulk momentum budget had not yet converged even at these very fine grids. Intriguingly, the comparison also showed that the large-eddy simulation is not automatically the more realistic reference: at 130 meters it resolved the shortest waves’ wavelength and phase but damped their amplitude, likely over-dissipating near-grid-scale wave energy, and it underestimated the vertical velocity fluctuations observed in the upper troposphere.

The practical implications reach well beyond academic curiosity. Turbulence in the upper troposphere and lower stratosphere is intermittent and localized, shaping stratosphere-troposphere exchange of greenhouse gases and pollutants and posing real hazards on long-haul routes that cross major mountain ranges. The study’s guidance is concrete: reliable simulation of small-scale mountain waves and turbulence at kilometer-scale resolution demands horizontal grid spacings of 1 kilometer or finer and vertical spacings of 200 meters or finer in the UTLS, while trapped lee waves and downstream wave structure remain stubbornly resolution-sensitive even then. Equally important, operational centers running kilometer-scale models over mountainous terrain should reconsider the empirical horizontal-shear and subgrid-orography terms of their TKE closures, which can inflate turbulence where none exists, or adopt alternatives like the two-energy scheme, which behaves stably in strongly stratified conditions without exhibiting the artifact. The authors caution that they do not claim the new scheme is more accurate everywhere, and genuine sub-kilometer turbulence downstream of the secondary ridge remained under-resolved in every configuration, including the large-eddy run. Future work will extend the analysis to additional DEEPWAVE cases and seek to couple the two-energy scheme with gravity-wave parameterizations, bridging the gap between explicitly resolved and parameterized wave-turbulence interactions in global and climate models, a step that could ultimately make turbulence forecasts that pilots and passengers depend on considerably more trustworthy.

Subject of Research: Simulation of mountain waves and turbulence in the upper troposphere and lower stratosphere using the ICON model at varying resolutions and turbulence schemes

Article Title: Impact of model resolution and turbulence scheme on the representation of mountain waves and turbulence

Article References: Impact of model resolution and turbulence scheme on the representation of mountain waves and turbulence. (n.d.). https://doi.org/10.5194/acp-26-13721-2026

Image Credits: AI Generated

DOI: 10.5194/acp-26-13721-2026

Keywords: mountain waves, gravity waves, turbulence, ICON model, DEEPWAVE, large-eddy simulation, turbulent kinetic energy, model resolution, upper troposphere, lower stratosphere, aviation safety, numerical weather prediction