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W1: Gravity Wave Parameterization for the Atmosphere

Principal investigators: Prof. Ulrich Achatz (Goethe University Frankfurt), Prof. Carsten Eden (Universität Hamburg), Prof. Franz-Josef Lübken (Leibniz Institute of Atmospheric Physics)

Present-day approaches to parameterize mesoscale motions in atmospheric models are oversimplified and over-tuned and hence not sufficiently reliable. Neither gravity-wave (GW) transience nor GW horizontal propagation is taken into account, although there is mounting evidence that they play a significant role. We will resolve these issues by the extension of the Lagrangian spectral GW model (MS-GWaM) in the atmosphere model ICON-a by lateral propagation and by the implementation of the related IDEMIX-a closure into the same model. 
While MS-GWaM is based on the fully resolved spectral GW energy equation, the related IDEMIX approach is simpler, but for the same reason also more efficient. Moreover, progress in GW-resolving modelling, using a novel dynamic macro-turbulence (DMS) parameterization, and lidar measurements in subproject T1 suggested merging these activities into W1. Highly resolved model and lidar data will be used for the validation of the parameterization approaches.

The following core themes will be in focus:

  1. Implementation of lateral propagation into MS-GWaM in ICON-a. Validation against lidar measurements and GW resolving simulations.
  2. Implementation of IDEMIX-a into ICON-a, including also lateral propagation. Validation against MS-GWaM, lidar data, and data from GW-resolving simulations.
  3. Extension of the DMS parameterization as a unified anisotropic closure scheme for atmospheric flows from the troposphere above the boundary layer to the upper mesosphere.
  4. Lidar observations covering the complete range of temporal and spatial scales relevant for GWs and the transition to turbulence, for the validation of the parameterizations.

The recently proposed parameterization module "Internal wave Dissipation Energy and MIXing" (IDEMIX) describes the generation, propagation, interaction, and dissipation of the internal gravity wave field and can be used in ocean general circulation models to account for vertical mixing (and friction) in the interior of the ocean. It is based on the radiative transfer equation of a weakly interacting internal wave field, for which spectrally integrated energy compartments are used as prognostic model variables. IDEMIX is central to the concept of an energetically consistent ocean model, since it enables to link all sources and sinks of internal wave energy and furthermore all parameterized forms of energy in an ocean model without spurious sources and sinks of energy.

Gravity waves are an important part of the energy cycle of the atmosphere and exchange momentum and energy with the mean flow due to wave breaking and wave refraction. Wave breaking and the resulting mean-flow effects need special parameterization in global climate models as they usually resolve at most a small part of the full spectrum of gravity waves. In W1 we apply the IDEMIX concept to develop corresponding gravity wave schemes for atmospheric circulation models. We propose to base a new, energetically consistent gravity wave parameterization on the radiative transfer equation for a field of waves. This method is fundamentally different from conventional schemes which describe the superposition of monochromatic waves launched at a particular level and which make the strong assumption of a stationary mean flow. As for the ocean, the wave field is represented by the wave-energy density in physical and wavenumber space. This new concept goes far beyond conventional gravity wave schemes which are based on the single column approximation. The radiative transfer equation has – to our knowledge – never been considered in the atmospheric community as a framework for sub-grid-scale parameterization. The proposed parameterization will, for the first time, 1) include all relevant sources continuously in space and time and 2) accommodate all gravity wave sources (orography, fronts, and convection) in a single parameterization framework. Moreover, the new scheme is formulated in a precisely energy preserving fashion.

The IDEMIX concept was shown to be successful for ocean applications but instead of focussing on the mixing effect by breaking waves as for the oceanic case, the focus in the atmospheric application is on the wave-mean flow interaction, i.e. the gravity wave drag and the energy deposition. We will extend the concept of energetically consistent closures to atmospheric gravity wave closures. The project will contribute to a transfer of knowledge from the oceanic community to the atmospheric community and vice versa.

A Memory of Pre-Pandemic Times and a Glimpse at the hopefully soon-to-be Future: My Visit at MIT and the AGU Fall Meeting 2021

With two successful talks, one on my research at the CRC181 and one on my science policy activities, I am more than happy with the received exposure and appreciation of our work.

Georg Sebastian Voelker, Postdoc in W1, S2

Having been in the home office for a long time during the last two years I am sure everyone wonders: Remember how things were before the virus hit? And how things will be afterwards? I was asking myself the very same questions while having a travel grant available I had won mid 2020 from the DFG research unit MS-GWaves which was still sitting in the accounts waiting to be used. My visit had been planned for a long time but had also been delayed by the pandemic. So when the US started opening up to foreign visitors in late summer 2021 I decided to try to move forward with the plan we had been setting aside for so long. And despite the restrictions and insecurities linked to long distance travel I should very soon be rewarded. On November 8 I boarded an airplane to Cambridge, Massachusetts to visit the long research partner of out group, Prof. Triantaphyllos Akylas at the Massachusetts Institute of Technology.

Our former and ongoing research project with T. R. Akylas is concerned with the background-modulated wave-wave interaction of internal gravity waves. In a previous manuscript we had been able to show that wave modulation by a sheared mean flow can significantly inhibit the energy exchange through a near-resonant triadic interaction. However, the assumptions of Boussinesq dynamics and a constant stratification limited the applicability of the findings to the atmospheric context. We thus took on the task to extend the theory to semi-incompressible dynamics with both a variable stratification and sheared mean winds. Having derived the theory beforehand we used the 5 weeks together at MIT to explore the combined effects of the modulation by the wind and the stratification on the wave interaction. Interestingly the two modulation mechanisms can counteract each other opening up the possibility of strong interactions in regions with both changing stratification and strong shear. As the tropopause region typically exhibits these features it is of particular interest to be studied. A manuscript is now in preparation and planned to be submitted later this year.

Having already traveled to the US another possibility opened for me: the in-person attendance of the fall meeting of the American Geophysical Union in New Orleans. Traveling to conferences has always been one of my favorite parts of being a scientist. I am particular fond of getting to know places and people, exchanging ideas about our research, networking among peers and like-minded people and making friends throughout the world. The idea of attending a conference on site for the first time in two years was therefore especially tempting for me. Even though it came with the huge insecurity of sharing the venue with another 10,000 people during a pandemic the stringent health policies helped keeping the participants safe and the number of infections low.

With two successful talks, one on my research at the CRC181 and one on my science policy activities, I am more than happy with the received exposure and appreciation of our work. Fostering existing connections and forging new ones additionally rendered the conference experience as a very positive one. But maybe most importantly, I also realized what I had been missing out in the past months. Even though video conferences can account for the majority of the scientific collaboration it will not be able to replace the experience of and the human relationships associated to a person to person contact. Partnerships are build on these relationships and I am hoping that there will be a time soon where we can find a way to get back together. Personally I feel motivated to move forward and make progress in ways that I had not expected when I boarded that airplane on November 8. I would therefore like to particularly thank the CRC181, the research group MS-GWaves, the WilhelmHeraeus Visiting Professorship program and not at last Prof. Ulrich Achatz and Prof. Triantaphyllos Akylas for enabling this collaboration and the conference participation for me.

Internal Gravity Wave Interaction, Propagation, and Breaking in the Atmosphere

It has becomes clear that, even though the vertical propagation of gravity waves may be dominant for many atmospheric phenomena, the horizontal propagation cannot be neglected.

Georg Sebastian Voelker, Postdoc W1

My name is Georg Sebastian and I am currently a postdoc in the TRRENERGYTRANSFERS, working in the project W1: “Gravity Wave Parameterization for the Atmosphere” under the supervision of Prof. Ulrich Achatz at the Goethe University Frankfurt am Main.

I had started out by studying the generation of internal gravity waves below the ocean surface by wind during my PhD under the supervision of Maren Walter. Recently, I moved to working on internal gravity waves in the atmosphere. Thus having studied both physical oceanography and atmospheric dynamics I am keen to investigate internal gravity waves in both environments considering various aspects of their dynamics.

The W1 Project is concerned with the lateral propagation of internal gravity waves in the atmosphere. In particular we employ the ray-tracing algorithm MS-GWaM to model sub-grid scale gravity waves including their transient propagation characteristics. That is, we model the lifetime of gravity waves including their interaction with the background – such as Doppler shifting or wave modulation by the mean flow.

In contrast, current state of the art parameterizations of gravity waves in atmospheric models assume that gravity waves propagate in the vertical instantaneously neglecting their finite vertical group velocity. Moreover these parameterizations do not allow for a horizontal propagation at all. However, it has becomes clear that, even though the vertical propagation of gravity waves may be dominant for many atmospheric phenomena, the horizontal propagation cannot be neglected. With the implementation of these effects in the numerical weather forecasting code ICON-NWP we hope to support that finding and gain new insight into the net effects and importance of the horizontal propagation.

Propagation is, however, only a part of a gravity wave’s life story. On its journey it can undergo a myriad of processes. Of special interest in various contexts are for instance the triad resonant interaction (TRI) and finally its breaking mechanisms.

Recently, we successfully described resonantly interacting gravity wave packets using a ray tracing algorithm utilizing weakly non-linear WBKJ theory in a Boussinesq environment including a slowly varying background flow. While interacting, the triad members are simultaneously modulated by a horizontal jet, leading to a reduction in energy exchange as the waves spectrally pass through the exact resonance conditions.

Moreover we are working on identifying instability mechanisms for strongly non-linear gravity waves in the vicinity of a mean-flow jet. Our theoretical study shows that in contrast to the upper jet edge the lower jet edge can sustain a novel type of modulational instability. New numerical evidence also shows that breaking mechanisms at the jet edges have distinct structures and might be associated to modulational instabilities or TRI (see Fig. 1 a and b).

This ongoing work is-among others–conducted in collaboration with Gergely Bölöni (DWD), Triantaphyllos Akylas (MIT, MA, USA), Mark Schlutow (FU Berlin, GER), and Ulrich Achatz (Goethe Universität Frankfurt).

Figure 1: Simulation of a strongly nonlinear, stationary internal gravity waves breaking in the vicinity of the lower (a) and upper (b) jet edge. Depicted are the vorticity and contours at a Richardson number Ri=0.25.