# W1: Gravity wave parameterisation for the atmosphere

Principal investigators: Prof. Erich Becker (Leibniz Institut for Atmospheric Physics), Prof. Carsten Eden (Universität Hamburg), Prof. Dirk Olbers (MARUM-AWI)

## Objectives

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.

## Invited Guests

## Reports

## 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.

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).

## Parameterising Gravity Wave Effects in the Atmosphere

Without the gravity wave parameterisations the models do not simulate these large scale reversals so the inclusion of gravity wave parameterisations are essential to Earth system models for future climate change predictions.

I am a postdoctoral researcher working on adapting the IDEMIX internal gravity wave model for the atmosphere in subproject W1 together with Carsten Eden, Dirk Olbers, Matthäus Mai and Erich Becker.

Internal gravity waves in the atmosphere have a profound effect on the large-scale circulation in the atmosphere and contribute significantly to the mesoscale wind and temperature variance. Since their scales are too small to be represented in general circulation models, their effects must be included via sub-grid scale parameterisations. Most climate and numerical weather prediction models now include some form of gravity wave parameterisation in order to accurately simulate large-scale middle-atmospheric phenomena such as the Brewer-Dobson circulation, the seasonal zonal-mean wind reversal and the quasi-biennial oscillation. Without the gravity wave parameterisations the models do not simulate these large scale reversals so the inclusion of gravity wave parameterisations are essential to Earth system models for future climate change predictions.

However current gravity wave parameterisations have a major drawback in that they use much too simplified physics to determine the feedback of the waves on the large scale flow. They are steady state and use separate parameterisations for terrain-generated and convectively-generated gravity waves. The main goal of this project is to include more sophisticated physics in atmospheric gravity wave parameterisations by use of IDEMIX which simulates the evolution in time of the wave field, its energy exchange interaction with the background flow (shown in Figure 1) and can accommodate multiple wave sources at once, allowing for wave-wave interactions.

IDEMIX can easily incorporate the effect of critical layers which occur frequently in the atmosphere since the gravity waves have similar phase speeds to the background flow, typically tens of metres per second. A dynamically-determined dissipation is calculated when the waves break, to keep the wave field within convective stability limits. The wave energetics from IDEMIX are used to calculate the gravity wave drag which feeds back onto the largescale circulation to either accelerate or decelerate it. Compared to traditional parameterisations which tend to provide the drag around the mesopause, IDEMIX exhibits a better vertical distribution of gravity wave drag throughout the middle atmosphere which is more fitting to observations. The basic IDEMIX for the atmosphere is now being implemented into the ICON-A component of the ICON Earth System Model.

## Publications

**Olbers, D.**, Jurgenowski, P., &**Eden, C.**(2020). A wind-driven model of the ocean surface layer with wave radiation physics.*Ocean Dynam.,*doi:**Olbers, D., Eden, C., Becker, E., Pollmann, F., & Jungclaus, J.**(2019). The IDEMIX Model: Parameterization of Internal Gravity Waves for Circulation Models of Ocean and Atmosphere. In*Energy Transfers in Atmosphere and Ocean*(pp. 87-125). Springer, Cham., doi: https://doi.org/10.1007/978-3-030-05704-6_3.**Pollmann, F.**,**Eden, C.**&**Olbers, D.**(2017). Evaluating the Global Internal Wave Model IDEMIX Using Finestructure Methods.*Am. Met. Soc.*, doi: 10.1175/JPO-D-16-0204.1.**Eden, C.**&**Olbers, D.**(2017). A closure for eddy-mean flow effects based on the Rossby wave energy equation.*Ocean Model.*,*114*, 59-71, doi: https://doi.org/10.1016/j.ocemod.2017.04.005.**Olbers, D.**&**Eden, C.**(2017). A closure for internal wave-mean flow interaction. Part A: Energy conversion.*J. Phys. Oceanogr.,*doi.org/10.1175/JPO-D-16-0054.1*.***Eden, C.**&**Olbers, D.**(2017). A closure for internal wave-mean flow interaction. Part B: Wave drag.*J. Phys. Oceanogr.,*doi: https://doi.org/10.1175/JPO-D-16-0056.1.