Parameterization 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 timescale separation between slow and fast degrees of freedom. We numerically compare the ensemble spread from a fixed initial condition, correlation functions and exit times from a domain. The weak coupling method gives more accurate results in all test cases, albeit with a higher numerical cost

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

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.Comment: 39 pages, 9 figures; This Work has been submitted to the Journal of Atmospheric Sciences. Copyright in this Work may be transferred without further notic

Numerical and experimental study of inertia-gravity waves in the differentially heated rotating annulus

International audienceThe occurrence and source mechanism of inertia-gravity waves (IGWs) are studied in the differentially heated rotating annulus via laboratory experiments (BTU) and numerical simulations (GUF). Two differentially heated rotating annulus experiments are used for this purpose at the BTU laboratories. The first is a modified version of the classical baroclinic experiment in which a juxtaposition of convective and motionless stratified layers can be created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid depth of the rotating tank, therefore baroclinic waves can only build up in thin layers located at the top and bottom, where the salt stratification is weakest. This new experimental setup, coined "barostrat instabil-ity", allows to study the exchange of momentum and energy between the layers, especially by the propagation of IGWs. Moreover, in contrast to the classical tank without salt stratification we have layers with N/f > 1. A ratio larger than unity implies that the IGW propagation in the experiment is expected to be qualitatively similar to the atmospheric case. Interestingly, we found local IGW packets along the jets in the surface and bottom layers where the local Rossby number is larger than 1, suggesting spontaneous imbalance as generating mechanism [1], and not boundary layer instability [2]. Theoretical considerations and numerical simulations have led to the identification of an annulus configuration, much wider and shallower, with a much larger temperature difference between the inner and outer cylinder walls, which is more atmosphere-like since it shows an N / f >1 even without the vertical salt stratification. Flow regime stability has been tested for this new differentially heated rotating annulus and compared with findings from the small tank. In view of the different geometries of the two experimental systems, their correspondence was excellent with respect to the large-scale. Moreover, direct numerical simulations were performed (GUF) for this atmosphere-like configuration of the experiment and possible regions of IGW activity were characterised by a Hilbert-transform algorithm. The simulations show a clear baroclinic wave structure exhibiting a realistic jet-front system superimposed by small-scale structures which are associated with IGWs occurring in wave packets [3]. The comparison of observations from a corresponding big tank experiment with numerical simulation shows that for both cases (as we already observed in the barostrat experiment), small scale wave packets are clearly correlated with an increased local Rossby number

Towards a numerical laboratory for investigations of gravity-wave 2 mean-ow interactions in the atmosphere

Idealized integral studies of the dynamics of atmospheric inertia-gravity waves (IGWs) from their sources in the troposphere (e.g., by spontaneous emission from jets and fronts) to dissipation and mean- ow e�ects at higher altitudes could contribute to a better treatment of these processes in IGW parameterizations in numerical weather prediction and climate simulation. It seems important that numerical codes applied for this purpose are e�cient and focus on the essentials. Therefore a previously published staggered-grid solver for f-plane soundproof pseudo-incompressible dynamics is extended here by two main components. These are 1) a semi-implicit time stepping scheme for the integration of buoyancy and Coriolis e�ects, and 2) the incorporation of Newtonian heating consistent with pseudo-incompressible dynamics. This heating function is used to enforce a temperature pro�le that is baroclinically unstable in the troposphere and it allows the background state to vary in time. Numerical experiments for several benchmarks are compared against a buoyancy/Coriolis-explicit third-order Runge-Kutta scheme, verifying the accuracy and ef- �ciency of the scheme. Preliminary mesoscale simulations with baroclinic-wave activity in the troposphere show intensive small-scale wave activity at high altitudes, and they also indicate there the expected reversal of the zonal-mean-zonal winds

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 MetStr\"om 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

Recent Progress in Modelling Imbalance in the Atmosphere and Ocean

Imbalance refers to the departure from the large-scale primarily vortical flows in the atmosphere and ocean whose motion is governed by a balance between Coriolis, pressure-gradient and buoyancy forces, and can be described approximately by quasi-geostrophic theory or similar balance models. Imbalanced motions are manifest either as fully nonlinear turbulence or as internal gravity waves which can extract energy from these geophysical flows but which can also feed energy back into the flows. Capturing the physics underlying these mechanisms is essential to understand how energy is transported from large geophysical scales ultimately to microscopic scales where it is dissipated. In the atmosphere it is also necessary for understanding momentum transport and its impact upon the mean wind and current speeds. During a February 2018 workshop at the Banff International Research Station (BIRS), atmospheric scientists, physical oceanographers, physicists and mathematicians gathered to discuss recent progress in understanding these processes through interpretation of observations, numerical simulations and mathematical modelling. The outcome of this meeting is reported upon here.We also wish to thank BIRS for their financial support and, in particular, the staff of BIRS for their excellent administration of the workshop. The authors gratefully acknowledge financial support by the following agencies: Achatz, German Research Foundation (DFG) for partial support through the research unit Multiscale Dynamics of Gravity Waves (MS-GWaves) and through Grants No. AC 71/8-2, No. AC 71/9-2, No. AC 71/10-2, No. AC 71/11-2, and No. AC 71/12-2; Caulfield, EPSRC Programme Grant No. EP/K034529/1 entitled “Mathematical Underpinnings of Stratified Turbulence;” Klymak, US Office of Naval Research (No. N00014-15-1-2585) and Natural Science and Engineering Research Council (NSERC) Discovery Grant No. 327920-2006; and Sutherland, NSERC Discovery Grant No. RGPIN-2015-04758

Neue Daten für die Sozialstaatsforschung : zur Konzeption der IAB-Panelerhebung "Arbeitsmarkt und Soziale Sicherung"

"Der Bericht resümiert die konzeptionellen und methodischen Vorarbeiten zur neuen Panelerhebung 'Arbeitsmarkt und Soziale Sicherung', die im Dezember 2006 erstmals ins Feld ging. Deren haushaltsbasierte Daten sollen dazu beitragen, eine wichtige Lücke im Bereich der Armuts- und Arbeitsmarktforschung zu schließen und wesentliche Befunde für die Wirkungsforschung zum SGB II zu liefern. Die Darstellung umfasst die konzeptionellen Vorüberlegungen bis hin zum modularen Aufbau des Erhebungsinstruments sowie eine Begründung der gegenüber früheren Ansätzen innovativen Stichprobengestaltung und deren Umsetzung in ein Forschungsdesign. Darüber hinaus wird ein mit dieser Panelerhebung verbundenes qualitatives Begleitprojekt vorgestellt, zu dessen Aufgaben die Feldexploration, die Entwicklung neuer Befragungsinstrumente und die Vertiefung statistischer Befunde gehören." (Autorenreferat, IAB-Doku) Inhaltsverzeichnis: Juliane Achatz, Andreas Hirseland, Markus Promberger: Rahmenkonzept für das IAB-Panel "Arbeitsmarkt und Soziale Sicherung (11-32); Rainer Schnell: Alternative Verfahren zur Stichprobengewinnung für ein Haushaltspanelsurvey mit Schwerpunkt im Niedrigeinkommens- und Transferleistungsbezug (33-59); Helmut Rudolph, Mark Trappmann: Design und Stichprobe des Panels "Arbeitsmarkt und Soziale Sicherung" (PASS) (60-101); Andreas Hirseland, Markus Promberger, Ulrich Wenzel: Armutsdynamik und Arbeitsmarkt: Qualitative Beobachtungen und Befragungen im Feld von Arbeitsmarkt und sozialer Sicherung (102-130).IAB-Haushaltspanel - Konzeption, empirische Sozialforschung, Erhebungsmethode, Stichprobe, soziale Sicherheit, Arbeitsmarktchancen, Niedrigeinkommen, Transferleistung

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