arXiv subjects

Ulrich Achatz

Publications and source records attributed to Ulrich Achatz.

14 recordsLinked to original sources

arXiv2026

Elastic Non-Uniform FFT (ENUFFT) spectral reconstruction of irregularly sampled orography on unstructured grids

Subgrid-scale orography remains a leading source of uncertainty in numerical modeling because terrain spectra must be recovered from irregularly sampled elevation data and then reduced to a flow-dependent launch budget for parameterizations. Existing approaches are limited either by assuming regular samples on rectangular grids or by fitting coefficients whose truncation and regularization effects become embedded in the spectrum. None achieves dynamic, flow-dependent truncation. This study introduces an Elastic Non-Uniform Fast Fourier Transform (ENUFFT) framework that computes local Fourier coefficients directly from irregularly sampled orography on unstructured grids, without interpolation or fitting. It combines a type-1 NUFFT with local windowing, quadrature weights, and a new Elastic Mode Selection (EMS) algorithm for retaining a local flow-dependent subset of modes. ENUFFT is compared with the strongest relevant existing method in a monochromatic and a real Alpine terrain test. In both cases, it recovers peak amplitude and direction comparably while significantly compacting the spectra (monochromatic ~25%, Alpine ~60%). It also satisfies the Parseval condition more closely with its spectral variance (energy) deviating from reference by ~14-24% versus ~500-122,000% for the existing method. Its EMS is additionally tested in a mountain-wave test where it reduces the launch spectrum by >=75% while keeping launch-power loss <=7%. Along with better compute scaling, ENUFFT is thus a computationally efficient, physically interpretable framework that can make Fourier-based orographic source descriptions practical for spectral-budget-aware parameterizations.

physics.ao-ph↗

arXiv2025

Impact of Non-Classical Gravity-Wave Dynamics on Middle-Atmosphere Mean Flow and Solar Tides

Conventional gravity-wave (GW) parameterizations neglect three aspects of GW dynamics. Instead of momentum and entropy fluxes they use Eliassen-Palm fluxes, thereby neglecting the possibility that resolved flow are not in geostrophic and hydrostatic balance. They neglect the transience of the GW field and of the resolved flow, by determining at every time step equilibrium profiles of GW fluxes that would result if the vertical GW propagation were instantaneous. Moreover, they also do not take into account lateral GW propagation and horizontal GW fluxes. Because the prognostic GW model MS-GWaM does not need to make these assumptions, it has been used in the global weather and climate code ICON to investigate their consequences for the simulation of monthly mean zonal mean flows and of solar tides. All three aspects are found to influence the simulation results significantly. Among those, transience and lateral propagation have the strongest impact. The mean circulation in the mesosphere and lower thermosphere is affected at all latitudes and in the stratosphere at high altitudes as well. This together with the directly modified GW forcing leads also to significant differences in the migrating and nonmigrating components of solar tides. Comparisons with tides retrieved from satellite data are most favorable if both aspects are taken into account. This argues for a correspondingly generalized treatment of GW dynamics in their parameterization, as an efficient alternative to GW permitting simulations.

physics.ao-ph↗

arXiv2025

The Impact of Non-Orographic Gravity Waves on Transport and Mixing: Effects of Oblique Propagation and Coupling to Turbulence

Gravity waves (GWs) are a fundamental driver of circulation, tracer transport, and mixing in the middle and upper atmosphere, but their treatment in global circulation models remains incomplete. In particular, standard parameterizations typically restrict propagation to the vertical and treat GW-turbulence interactions in only a rudimentary manner, potentially leading to systematic biases in simulated dynamics and transport. Here, we use the Multi-Scale Gravity-Wave Model (MS-GWaM) implemented in the Community Climate Icosahedral Nonhydrostatic Model UA-ICON, together with a novel theoretical framework, to quantify the impact of (i) oblique GW propagation and (ii) explicit bidirectional coupling between GWs and turbulence. Ensemble simulations reveal that allowing for oblique propagation lowers and cools the summer mesopause by shifting the deposition of momentum and heat to lower altitudes, reduces GW-induced vertical shear in the the middle and lower atmosphere, and enhances turbulent kinetic energy in the upper mesosphere and lower thermosphere. In contrast, coupling GWs to turbulence produces a nearly opposite mesopause response, lifting and warming the mesopause, while maintaining a reduction in wave-induced shear and further enhancing turbulence. Tracer experiments additionally show that turbulent coupling significantly increases mixing, particularly in regions of enhanced TKE, with implications for chemical redistribution. These results demonstrate that both oblique GW propagation and GW-turbulence interactions exert leading-order controls on mesosphere-lower thermosphere circulation, temperature structure, and tracer transport. Neglecting these processes in global models likely contributes to biases in the Brewer-Dobson circulation, energy balance, and constituent distributions, underscoring the need for next-generation GW parameterizations that capture these effects.

physics.ao-ph↗

arXiv2025

Impact of Small-Scale Gravity Waves on Tracer Transport

Small-scale gravity waves, with horizontal wavelengths of up to a few hundred kilometers and vertical wavelengths of up to a few kilometers, play a crucial role in atmospheric tracer transport. However, their effects remain unresolved in climate models and must be parameterized. This study investigates how gravity waves influence large-scale tracer distributions, utilizing a multiple-scale analysis to systematically identify the governing terms of gravity wave-induced tracer fluxes. The analysis reveals both leading-order and next-order impacts: the former being the inertia-gravity wave-induced tracer Stokes drift, which acts perpendicular to both the large-scale tracer gradient and the wave number, while the latter becomes significant at lower latitudes where Coriolis effects diminish. A numerical framework is developed to incorporate these fluxes into a gravity wave parameterization model, potentially enhancing climate model accuracy without requiring explicit resolution of small-scale wave dynamics. Model validation against high-resolution wave-resolving simulations confirms the effectiveness of this approach. By improving the representation of gravity wave-induced tracer transport, this research advances the accuracy of climate simulations, particularly in their depiction of microphysics and radiative processes.

physics.ao-ph↗

arXiv2024

The impact of transience in the interaction between orographic gravity waves and mean flow

A Lagrangian gravity-wave parameterization (MS-GWaM, Multi-Scale Gravity-Wave Model) that allows for fully transient wave-mean-flow interaction and horizontal propagation is applied to orographic gravity waves for the first time. Both linear and nonlinear mountain waves are modeled in idealized simulations within the pseudo-incompressible flow solver PincFlow. Two-dimensional flows over monochromatic orographies are considered, using MS-GWaM either in its fully transient implementation or in a steady-state implementation that represents classic mountain-wave parameterizations. Comparisons of wave-resolving simulations (not using MS-GWaM) and coarse-resolution simulations (using MS-GWaM) show that allowing for transience leads to a significantly more accurate forcing of the resolved mean flow. The model is able to reproduce the transient forcing of linearly generated mountain waves that slowly propagate upwards, in contrast to the instantaneous distribution of wave energy in classic parameterizations. At high altitudes, wave breaking induces a wind reversal that is captured by the transient model but inhibited in steady-state simulations, due to the assumption of critical level formation. This shows that transience can have a substantial impact in the interaction between mountain waves and mean flow.

physics.flu-dyn↗

arXiv2024

Crucial Role of Obliquely Propagating Gravity Waves in the Quasi-Biennial Oscillation Dynamics

In climate modelling, the reality of simulated flows in the middle atmosphere is largely affected by the model's representation of gravity wave processes that are unresolved, while these processes are usually simplified to facilitate computations. The simplification commonly applied in existing climate models is to neglect wave propagation in horizontal direction and time. Here we use a model that fully represents the propagation of unresolved waves in all directions, thereby elucidating its dynamical effect upon the most important climate mode in the tropical stratosphere, namely the quasi-biennial oscillation. Our simulation shows that the waves at the equatorial stratosphere, which are known to drive this climate mode, can originate far away from the equator in the troposphere. The waves propagating obliquely toward the equator are found to play a huge role in the phase progression of the quasi-biennial oscillation as well as in its penetration into the lower stratosphere. Such waves will require further attention, given that current climate models are struggling to simulate the quasi-biennial oscillation down to the lower stratosphere, which may be needed to reproduce its observed impacts on the surface climate.

physics.ao-ph↗

arXiv2024

A Constrained Spectral Approximation of Subgrid-Scale Orography on Unstructured Grids

The representation of subgrid-scale orography is a challenge in the physical parameterization of orographic gravity-wave sources in weather forecasting. A significant hurdle is encoding as much physical information with as simple a representation as possible. Other issues include scale awareness, i.e., the orographic representation has to change according to the grid cell size and usability on unstructured geodesic grids with non-quadrilateral grid cells. This work introduces a novel spectral analysis method approximating a scale-aware spectrum of subgrid-scale orography on unstructured geodesic grids. The dimension of the physical orographic data is reduced by more than two orders of magnitude in its spectral representation. Simultaneously, the power of the approximated spectrum is close to the physical value. The method is based on well-known least-squares spectral analyses. However, it is robust to the choice of the free parameters, and tuning the algorithm is generally unnecessary. Numerical experiments involving an idealized setup show that this novel spectral analysis performs significantly better than a straightforward least-squares spectral analysis in representing the physical energy of a spectrum. Studies involving real-world topographic data are conducted, and reasonable error scores within $\pm 10\%$ error relative to the maximum physical quantity of interest are achieved across different grid sizes and background wind speeds. The deterministic behavior of the method is investigated along with its principal capabilities and potential biases, and it is shown that the error scores can be iteratively improved if an optimization target is known. Discussions on the method's limitations and broader applicability conclude this work.

physics.ao-ph↗

arXiv2024

MS-GWaM: A 3-dimensional transient gravity wave parametrization for atmospheric models

Parametrizations for internal gravity waves in atmospheric models are traditionally subject to a number of simplifications. Most notably, they rely on both neglecting wave propagation and advection in the horizontal direction (single-column assumption) and an instantaneous balance in the vertical direction (steady-state assumption). While these simplifications are well justified to cover some essential dynamic effects and keep the computational effort small it has been shown that both mechanisms are potentially significant. In particular, the recently introduced Multiscale Gravity Wave Model (MS-GWaM) successfully applied ray tracing methods in a novel type of transient but columnar internal gravity wave parameterization (MS-GWaM-1D). We extend this concept to a three-dimensional version of the parameterization (MS-GWaM-3D) to simulate subgrid-scale non-orographic internal gravity waves. The resulting global wave model -- implemented into the weather-forecast and climate code ICON -- contains three-dimensional transient propagation with accurate flux calculations, a latitude-dependent background source, and convectively generated waves. MS-GWaM-3D helps reproducing expected temperature and wind patterns in the mesopause region in the climatological zonal mean state and thus proves a viable IGW parameterization. Analyzing the global wave action budget, we find that horizontal wave propagation is as important as vertical wave propagation. The corresponding wave refraction includes previously missing but well-known effects such as wave refraction into the polar jet streams. On a global scale, three-dimensional wave refraction leads to a horizontal flow-dependent redistribution of waves such that the structures of the zonal mean wave drag and consequently the zonal mean winds are modified.

physics.flu-dyn↗

arXiv2023

Interactions between gravity waves and cirrus clouds: asymptotic modeling of wave induced ice nucleation

We present an asymptotic approach for the systematic investigation of the effect of gravity waves (GW) on ice clouds formed through homogeneous nucleation. In particular, we consider high- and mid-frequency GW in the tropopause region driving the formation of ice clouds, modeled with a double-moment bulk ice microphysics scheme. The asymptotic approach allows for identifying reduced equations for self-consistent description of the ice dynamics forced by GW including the effects of diffusional growth and nucleation of ice crystals. Further, corresponding analytical solutions for a monochromatic GW are derived under a single-parcel approximation. It is demonstrated that the asymptotic solutions capture the dynamics of the full ice model and provide a simple expression for the nucleated number of ice crystals. The present approach is extended to allow for superposition of GW, as well as, for variable mean mass in the ice crystal distribution. Implications of the results for an improved representation of GW variability in cirrus parameterizations are discussed.

physics.ao-ph↗

arXiv2023

Multi-Scale Dynamics of the Interaction Between Waves and Mean Flows: From Nonlinear WKB Theory to Gravity-Wave Parameterizations in Weather and Climate Models

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The development of this theory is reviewed here. It applies to all interesting regimes of atmospheric stratification, i.e. also to moderately strong stratification as occurring in the middle atmosphere, and thereby extends classic assumptions for the derivation of quasi-geostrophic theory. At strong wave amplitudes a fully nonlinear theory arises that is complemented by a quasilinear theory for weak GW amplitudes. The latter allows the extension to a spectral description that forms the basis of numerical implementations that avoid instabilities due to caustics, e.g. from GW reflection. Conservation properties are discussed, for energy and potential vorticity, as well as conditions under which a GW impact on the larger-scale flow is possible. The numerical implementation of the theory for GW parameterizations in atmospheric models is described, and the consequences of the approach are discussed, as compared to classic GW parameterizations. Although more costly than the latter, it exhibits significantly enhanced realism, while being considerably more efficient than an approach where all relevant GWs are to be resolved. The reported theory and its implementation might be of interest also for the efficient and conceptually insightful description of other wave-mean interactions, including those where the formation of caustics presents a special challenge.

physics.ao-ph↗

arXiv2018

Stochastic subgrid-scale parameterization for one-dimensional shallow water dynamics using stochastic mode reduction

We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in physical space by defining resolved variables as local spatial averages over finite-volume cells and unresolved variables as corresponding residuals. Based on the assumption of a time-scale separation between the slow spatial averages and the fast residuals, the stochastic mode reduction procedure is used to obtain a low-resolution model for the spatial averages alone with local stochastic subgrid-scale parameterization coupling each resolved variable only to a few neighboring cells. The closure improves the results of the low-resolution model and outperforms two purely empirical stochastic parameterizations. It is shown that the largest benefit is in the representation of the energy spectrum. By adjusting only a single coefficient (the strength of the noise) we observe that there is a potential for improving the performance of the parameterization, if additional tuning of the coefficients is performed. In addition, the scale-awareness of the parameterizations is studied.

physics.flu-dyn↗

arXiv2017

Stochastic Parameterization: Towards a new view of Weather and Climate Models

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined.

physics.ao-ph↗

arXiv2016

Parametrization of stochastic multiscale triads

We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system, we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large time scale separation between slow and fast degrees of freedom. We look at ensemble spread from a fixed initial condition, correlation functions and exit times from domain. The weak coupling method gives better results in all test cases, albeit with a higher numerical cost.

cond-mat.stat-mech↗

arXiv2014

Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics

The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain ``benchmarks'' have been created that can later be used as test cases for atmospheric numerical model validation.

physics.flu-dyn↗