In the presence of a strong midlatitude jet, Rossby waves are ducted along the jet in the zonal direction. If enough wave activity manages to travel all the way around the Earth, the wave may super-impose with itself and, hence, increase in amplitude. This is the essence of Rossby wave resonance.

I our group, we have worked about several aspects of Rossby wave resonance, and for us this remains an active area of research up to date.

V. Wirth, 2020: Waveguidability of idealized midlatitude jets and the limitations of ray tracing theory In this paper we investigated the waveguidability of Rossby waves along a circumglobal midlatitude jet. It turns out that waveguidability increases smoothly as the jet strength increases or the jet width decreases. This result is in stark contrast with a popular method to diagnose Rossby waveguides which is based on refractive index theory and which provides a binary result, i.e., either a “waveguide” or “no waveguide”.

V. Wirth and C. Polster, 2021: The problem of diagnosing jet waveguidability in the presence of large-amplitude eddies As it turns out, the choice of the background state in linear theory plays a key role for diagnosing Rossby waveguides. In this paper we contrasted the simple zonal average with the so-called “zonalized wind”. The latter is part of the Modified Lagrangian Mean state; it can be obtained through conservative symmetrization of the potential vorticity field and ensuing potential vorticity inversion. It was shown that these two basic states may be very different in the presence of large amplitude waves.

R. H. White, K. Kornhuber, O. Martius, and V. Wirth, 2022: From atmospheric waves to heatwaves: A waveguide perspective for understanding and predicting concurrent, persistent and extreme extratropical weather This paper is an opinion piece about the connection between high-impact weather extremes and upper tropospheric Rossby waves on the jet stream. The issue is motivated by the rather low confidence in subseasonal-to-seasonal predictions for these events as well as the changes expected in a warmer climate. It is suggested that a new focus on the waveguiding properties of the jet, the resulting properties of the waves, and their impact on the surface conditions may help to make progress with some of the pressing questions.

A. Segalini, J. Riboldi, V. Wirth, and G. Messori, 2024: A linear assessment of barotropic Rossby wave propagation in different background flow configurations This paper can be considered as a follow-up to Wirth (2020). It presents an improved algorithm to solve the linear barotropic vorticity equation on the sphere in a forced-dissipative configuration. The algorithm allows one to systematically study the waveguiding properties of specified basic states. The paper also extends the results of Wirth (2020) by exploring several single- and double-jet basic states with respect to their waveguidability.

N. Harnik and V. Wirth, 2025: Quasi-resonance in a leaky waveguide? In this paper, we solved a very idealized problem that allowed us to obtain analytical solutions with the goal to better understand Rossby wave resonance. As it turns out, the solution in a leaky waveguide without damping has rather similar properties as the solution in a perfect waveguide in the presence of damping. We also computed numerical solutions for basic states that are characterized by a strong midlatitude jet, and we discussed similarities and differences with respect to the analytical solutions. As a main result we found that a strong midlatitude jet acts like a leaky (rather than a perfect) waveguide.

Over recent years, our group has developed an interest in Noboru Nakamura’s finite-amplitude wave activity framework. We extended and applied this framework to diagnose large-amplitude Rossby waves in the upper troposphere and to define a novel eddy-free background state that varies smoothly in longitude.

P. Ghinassi, G. Frakoulidis, and V. Wirth, 2018: Local finite amplitude wave activity as a diagnostic for Rossby wave packets In this paper we followed the footsteps of Noboru Nakamura and suggested a novel variant of finite amplitude local wave activity that applies to the primitive-equation framework in isentropic coordinates. The novel diagnostic was subsequently applied to follow upper tropospheric Rossby wave packets, and it was compared with more traditional diagnostics based on the wave packet envelope. It turns out that local finite amplitude wave activity has some desirable properties especially in case of large-amplitude waves.

P. Ghinassi, M. Baumgart, F. Teubler, M. Riemer, and V. Wirth. 2020: A budget equation for the amplitude of Rossby wave packets based on finite amplitude local wave activity Building on Ghinassi et al. (2018), we used their framework to investigate the dynamics of Rossby wave packets, distinguishing the role of conservative from non-conservative processes. Forecast errors were linked to misrepresentations of diabatic processes and upper-level divergent outflow.

C. Polster and V. Wirth, 2023: The onset of a blocking event as a “traffic jam”: Characterization with ensemble sensitivity analysis We tested Nakamura’s “traffic jam” theory for blocking onset using finite-amplitude local wave activity and ensemble sensitivity analysis applied to reanalysis data. Blocking onset was sensitive to upstream wave activity 1.5 days prior to the onset — consistent with theory. Similarly, scatter plots of the finite amplitude wave activity flux against finite amplitude wave activity indicate a similar behavior as hypothesized in Noboru’s idealized theory. At the same time, it transpires that this simple one-dimensional traffic-jam theory is unable to represent the higher-dimensional aspects of block formation.

C. Polster and V. Wirth, 2023: A new atmospheric background state to diagnose local waveguidability We proposed a novel zonally varying eddy-free background state, generalizing the “zonalized wind” from the Modified Lagrangian Mean. For this purpose, Ertel Potential vorticity is redistributed conservatively in a rolling window so as to render it zonally symmetric within the window; thereafter, the window is shifted in the zonal direction and the procedure is repeated. Our novel background state shows important characteristics of climatological waveguide structures, but in contrast with earlier methods it can be applied to snapshots of atmospheric data.

We aim at understanding atmospheric predictability from a dynamics-based perspective by investigating the error-growth mechanisms that govern predictability for different scales, weather systems, and climatological regions.

Banner Clouds are clouds in the lee of steep mountains or sharp ridges. Their occurrence is somewhat counterintuitive: when a parcel approaches a mountain or a mountain ridge, one expects lifting, and, hence, a cloud on the windward side. Apparently, the opposite is true in case of a banner cloud, indicating that the lifting in the lee must be larger than the lifting on the windward side. Pertinent questions are: under what circumstances can one expect stronger uplift in the lee than on the windward side? Why? How exactly does it work?

In our group we have been working about this topic during the past 20 years.

J. H. Schween, J. Kuettner, D. Reinert, J. Reuder, and V. Wirth, 2007: Definition of “banner clouds” based on time lapse movies Our starting point was a project where we used time lapse movies taken at the Mt. Zugspitze in the Bavarian Alps to come up with a sound definition of the term “banner cloud”. A fun fact about this paper is that we included a number of these time lapse movies in the form of mpeg files.

D. Reinert and V. Wirth, 2009: A new LES model for simulating air flow and warm clouds above highly complex terrain. Part II: The moist model. Boundary Layer Meteorology Later we started to perform Large-Eddy Simulations (LES) to learn more about this interesting phenomenon. In this paper we showed that the problem can, to a first approximation, be investigated by considering the flow of dry air past a mountain; in other words: the latent heat release within the cloud does not have a large impact on the structure of the flow and can, therefore, be neglected for conceptual clarity. Correspondingly, we suggested the use of the Lagrangian vertical uplift and its leeward-windward asymmetry as an approximate but robust diagnostic for the occurrence of banner clouds.

V. Wirth, M. Kristen, M. Leschner, J. Reuder, and J. H. Schween, 2012: Banner clouds observed at Mount ZugspitzeIn the meantime, we had carried through various measurements at Mt. Zugspitze in the Bavarian Alps, allowing us to investigate banner clouds in more detail at this particular site. Amongst others, a webcam was mounted at the observatory right on the summit of this mountain. The webcam was operated over the duration of almost four years. This simple device, in combination with the routine measurements from the mountain’s summit, turned out to be very valuable to obtain statistics about the diurnal and the seasonal cycle of banner clouds at Mt. Zugspitze.

M. Voigt and V. Wirth, 2013: Mechanisms of Banner Cloud Formation Around the same time, we applied Large Eddy Simulation in an idealized model configuration to illuminate the mechanisms of banner cloud formation. Amongst the three candidate mechanisms (lee-side uplift, mixing fog, and the Bernoulli effect), vertical uplift turned out to be quantitatively by far the dominant mechanism. In the same paper we published a cartoon which visualizes the salient features of flow past an isolated mountain that are conducive to banner cloud formation.

S. Schappert and V. Wirth, 2015: Origin and flow history of air parcels in orographic banner clouds In subsequent work we turned our attention to computing trajectories to illuminate the Lagrangian properties of those air parcels that end up forming the banner cloud. In that paper we also quantified the amount of mixing that a parcel experiences on its way into the cloud.

I. Prestel and V. Wirth, 2016: What flow conditions are conducive to banner cloud formation? As our next step, we set up idealized large-eddy simulations in a parameter-sweep configuration allowing us to systematically explore the conditions that are conducive to banner cloud formation. As it turns out, a regime diagram published earlier by P. Baines turned out to be helpful. Although this regime diagram was based on the results from laboratory experiments with flow past a two-dimensional obstacle, our simulations showed that these regimes also apply to flow past an isolated three-dimensional mountain. Subsequently, this allowed us to search for the part of the regime diagram with a large windward-leeward asymmetry of the Lagrangian vertical uplift. As it turns out, favorable conditions for banner cloud formation require the presence of a steep mountain and a weekly or neutrally stratified ambient atmosphere.

V. Wirth, P. Bubel, J. Eichhorn, E. Schoemer, T. Kremer, R. Erbes, S. Schappert, and I. Prestel, 2020: The role of wind speed and wind shear for banner cloud formation A similar idealized model configuration as in previous papers was later used to explore the sensitivity of banner cloud formation to the strength and the shear of the ambient flow. One highlight from this work was the recognition that wind shear can have a profound impact on the shape of the leeward vortex, and yet that in both cases (shear vs. no shear) the occurrence of a lee-side cloud is a rather robust phenomenon. The sensitive dependence of the vortex structures motivated subsequent investigations with more realistic orographies as well as the design of a dedicated measurement campaign.

M. L. Thomas and V. Wirth, 2023: Sensitivity of banner cloud formation to orography and the ambient atmosphere: Transition from idealized to more realistic scenarios Motivated by our earlier studies, we investigated the change of the flow patterns and the potential for banner cloud formation as one changes the orography from idealized over semi-realistic to realistic. Focus of that study was the specific orography of the Matterhorn in the Swiss Alps. We found that the lee-side flow patterns sensitively depend on the exact shape of the Matterhorn, and that some of the prototypical features found for pyramid-shaped orography vanish altogether as one transitions from idealized to more realistic orography. At the same time, the potential for banner cloud formation turned out to be particularly high in case of the fully realistic Matterhorn orography, and the ridges and valleys in the intermediate environment of the mountain appeared to play an important role.

S. W. Hoch, M. L. Thomas, H. Huwald, M. Lehning, B. J. A. van Schaik, P. Imbert, D. S. Rentel, and V. Wirth, 2025: The MatterHEX experiment – Investigating atmospheric flow patterns in highly complex terrain related to banner cloud formation The Matterhorn in the Swiss Alps is a mountain with spectacular and frequent banner cloud occurrences. For this reason, we decided to design a measurement campaign at this mountain (called: MatterHEX) to put our previous results to a test. Key instrument was a scanning Doppler lidar to retrieve wind speed along the line of sight, augmented by radiosonde ascents to characterize the ambient atmosphere as well as webcams to obtain a visual impression of occurring cloud phenomena. In essence we could show that, indeed, there is a conspicuous return flow in the lee of the Matterhorn, which is consistent with our Large Eddy simulations and which is essential for the lee-side uplift.

M. Thomas, S. Hoch, H. Huwald, M. Lehning, B. J. A. van Schaik, P. Imbert, D. S. Rentel, and V. Wirth, 2025: Banner cloud formation at the Matterhorn: Measurements versus large-eddy simulations At the same time, we did extensive large eddy simulations of flow past the realistic Matterhorn orography. This work allowed us to compare the results from the MatterHEX measurements with those from the large eddy simulations. It turned out that the flow field in our simulations showed the same key features as the observed wind field, most notably the return flow in the lee of the mountain and the accompanying vertical uplift. This corroborates many of our findings from previous simulations with more idealized model configurations, indicating that the earlier results must be relevant in a realistic setting, too.

Heat waves can have major impacts on both society and the environment, yet their underlying physical formation mechanisms are not fully understood. In particular, there is ongoing debate regarding the relative contributions of three key processes: horizontal advection, subsidence, and diabatic heating. Using a recently developed technique based on passive tracer advection (Mayer and Wirth (2023)), we quantified the importance of these processes from a Lagrangian perspective. Our approach introduces a novel way of assessing the contributions by comparing them against their climatological contributions. Both case studies (Mayer and Wirth (2025)) and a global analysis (Mayer (2025)) show that anomalous horizontal advection—specifically the absence of cold-air advection—rather than anomalous subsidence or diabatic heating, can be seen as the key contributor to heat extremes in the midlatitudes.

This project investigates the upscale growth and amplification of forecast uncertainty in the mid-latitudes using data from dedicated numerical experiments and quantitative process-based analysis. The processes that govern the projection of convective-scale uncertainty on larger scales are examined in detail. One focus is on characterizing this upscale growth for different weather situations. Our publication on identifying and tracking coherent regions of forecast uncertainty can be found here.

The project is carried out in collaboration with the LMU Munich. Funded by the DFG. Period: November 2025 to October 2028.