## Gravity waves in the atmosphere

Internal gravity waves (GWs) play a significant role in atmospheric dynamics. Being radiated from various processes in the atmosphere, the field of interest for this research initiative, many of them are typically too small in scale to be explicitly describable in current-resolution numerical weather prediction (NWP) and climate models. Their effects, however, matter on many spatial scales so that they pose an important multi-scale problem to atmospheric dynamics.

**Different layers of the atmosphere show up with different GW effects:**

*Lower atmosphere:*

GW effects in the lower atmosphere are manifold. Examples are the impact of small-scale GWs of orographic origin on the predicted larger-scale flow, parameterized via suitably formulated parameterization schemes, clear-air turbulence generated by breaking GWs, and the GW impact on high cirrus clouds and polar stratospheric clouds.*Middle atmosphere:*

Even more direct than in the lower atmosphere, however, are GW effects in the middle atmosphere. The mesosphere is marked by a strong departure of the temperature field from its radiative equilibrium. This, accompanied via thermal-wind balance by a corresponding impact on the zonal winds, is probably the most prominent effect of GW breaking and the associated momentum and energy deposition in the atmosphere.

The extent to which GWs control the mesosphere circulation also seems to be of great relevance both to medium-range weather forecast and climate modeling in the troposphere. That circulation influences, via ‘downward control’ also the lower layers. Indeed, there is evidence for the importance of the middle atmosphere for long-range forecasting of winter weather in the northern hemisphere. GW dynamics in the stratosphere is critical as well. It has been shown that variations in the orographic gravity wave drag (OGWD) have a direct influence both on the climate of the troposphere and on the temperature variability in the stratosphere, as discussed in and the references therein. The latter has important implications for stratospheric ozone chemistry. Finally we mention the role played by GWs in the dynamics of large-scale waves, e.g. the quasi-biennial oscillation (QBO), a significant element of stratospheric variability in the tropics. As known from observations, the QBO phase impacts the stratospheric winter polar vortex and, via downward coupling, the surface winter weather in e.g. Europe. This could provide an interesting pathway to seasonal prediction. Already today the QBO can be predicted well several months ahead, and there are indications that improved models may predict it with several years lead-time. The QBO, however, is driven to more than 50% by GWs.

**GW processes:**

**Gravity wave Sources and their representation in numerical models:**

- Orographic GWs: generated by flow over topography:

The representation of orographic GW effects in atmospheric models suffers from simplifications. For instance, in the present single-column approach parameterized mountain waves are assumed to propagate vertically whereas real mountain waves, propagate leeward of South America and the Antarctic Peninsula into the Drake Passage, e.g., thus providing drag where no orography is found. Mountain waves are also highly intermittent, generating large bursts in momentum flux even relevant to the hemispheric mean. A strength of available OGWD schemes certainly is that they are flow-dependent, as might be important for the applicability to climate-change problems. - Non-orographic GWs:
- Convective processes:

Recently, progress to a similar level of theoretical understanding and skill of the available schemes has been made with regard to GW radiation from convective sources. Based on linear theory, latent heat release from the convective subgrid-scale (SGS) parameterization of a model is taken, to predict the GWs emitted from the corresponding processes. Additional work is needed, however, since at present the GWs emitted considerably depend on the details of the convective SGS scheme. At least this has been shown for resolved GWs, and there is no reason to assume that the situation differs in the case of SGS GWs. Even within single schemes there still is an uncomfortably large number of insufficiently constrained parameters. In some schemes these are the horizontal extent and dominant temporal scale of convection, which depend on the process considered. More detailed measurements of GWs from convective sources is desirable to better constrain available schemes for convective GWs. Constraints, however, can also be derived from global satellite measurements. - Spontaneous imbalance:

Much less developed is the parameterization of other relevant sources. Among these, spontaneous imbalance of synoptic-scale flow might be most important. Recent work indicates that much of this process can be understood by forced tangent-linear dynamics. - Kelvin-Helmholtz turbulence
- GW breaking

- Convective processes:

Even interactions between such processes exist, e.g. the convective enhancement of spontaneous imbalance, so that ultimately a common scheme for GW generation and propagation would be desirable, based on a unified theory that takes these interactions into account.

**Gravity wave propagation:**

The GW propagation from their sources to where they interact with the large-scale flow is usually treated using Wentzel-Kramers-Brillouin (WKB) theory. The development of local wave characteristics, i.e amplitude and wave number, are predicted along rays propagating at the local group velocity. For efficiency reasons two essential simplifying assumptions are made: (1) Horizontal wave propagation and the impact of horizontal gradients in the resolved flow are neglected. (2) Along a vertical column the wave fields are adjusted immediately to a steady-state profile which one could only get with steady-state sources and steady-state resolved flow and after a time longer than that needed by GWs to propagate from the sources to the model top. There are several reasons why this is to be improved. As a result of horizontal gradients in the resolved flow GWs are known to be focused into the jets. This has both been predicted by theory and observed, both in satellite and in radiosonde data. Horizontal propagation can be expected to have a notable effect on GW amplitudes. Indeed, data from a GW-permitting global model show lateral propagation of GWs to be an important factor in the GW momentum fluxes. Recent work has addressed some of these issues also in a GW parameterization, demonstrating that the resulting modifications are significant. Moreover, while the assumption of an instantaneously adjusted steady-state vertical profile becomes less trustworthy when the middle atmosphere is included into a model, and thus the model top raised, the transience of GW momentum fluxes does already appear to be significant in the lower stratosphere, as super-pressure balloon data indicate. This effect seems to be strongest over mountains but it can be assumed that variable convection, e.g. by a diurnal cycle, has an impact. Similar effects also occur in the interaction between GWs and solar tides. An attempt at taking vertical propagation effects and source transience into account is the inclusion of an intermittency factor, another option would be a prognostic GW model, treating these processes explicitly. Another important problem we are facing at present model resolutions is that part of the GW spectrum is resolved, while another part is simply neglected. It is all but clear that it would not be better to also take the effects of these unresolved GWs into account. There are indications that the GW momentum flux, essential for the GW impact on the synoptic-scale flow, has significant contributions from these small scales. High-resolution NWP models, moreover, are known to perform sub-optimal without orographic GW parameterizations. Then, instead of propagating on a synoptic-scale background, as was assumed when the original WKB theory was developed, unresolved GWs propagate on a background that includes other GWs. These have both large spatial gradients, due to their short wavelengths, and short time scales. This is a completely new situation which at least requires dropping the simplifying assumptions used so far, and actually might even need reconsideration of the basic theory. Encouraging steps into this direction have been taken by [AKS10] who have developed a multi-scale asymptotic approach for the derivation of a nonlinear large-amplitude WKB theory. Once wave transience is allowed, possibly important quasi-linear effects such as self-acceleration are included at no additional cost. Likewise, present WKB theory is not able to handle sharp gradients correctly, as e.g. encountered by GWs propagating through the tropopause. Within this quite thin layer the stratification changes significantly. In addition, the horizontal wind may change due to considerable shear. Mixing layers might also occur close to the tropopause, induced by dynamic instabilities. Thus, the properties of the tropopause region decide about partial reflection, trapping of GWs from below as well as non-linear wave generation and interaction. These effects have so far not been investigated in detail although they are crucial for GW spectra in the lowermost stratosphere and the further upward propagation of GWs into stratosphere and mesosphere.

** Gravity wave dissipation:**

Similar is the situation with regard to GW dissipation. A common assumption used in GW parameterizations is that wave breaking sets in at amplitudes yielding the wave either statically or at least dynamically unstable. By now we know that wave breaking sets in considerably below these thresholds and that the momentum deposition ensuing is stronger than implied by just keeping the GWs at the conventional saturation thresholds. The results from these stability analyses and direct numerical simulations (DNS) have so far not found their way into a parameterization of GW dissipation. Moreover, the mentioned studies typically use Boussinesq theory, and thus analyze GWs at given initial amplitude. Once the instability, triggered by some initial perturbation, has set in, the wave amplitude decays due to the turbulent impact. In the real atmosphere, however, an upward propagating wave experiences a competition between wave growth, due to the ambient density gradient, and wave decay, due to the instability. Various publications report simulations of upward propagating GWs which eventually break], but none analyze this competition, and derive from it a corresponding parameterization, in terms of the essential instability modes triggering it, and their nonlinear development which is at the heart of the wave breaking process. To this competition modulational instability could add important new aspects, as it is able to locally enhance the GW amplitude.

**Correct answer for the wrong reasons**?

A tempting approach to the issues listed above could be an attempt to re-tune available schemes, possibly by means of data assimilation techniques. However, most schemes can be made to perform well with regard to the large-scale circulation they produce. Different schemes use different approximations of GW dynamics. Therefore no more than one of them can be giving the correct answer for the right reasons. It is unclear how much of the success of available schemes is due to parameter over-tuning, and there is a risk that apparently successful schemes will eventually have problems in climate-change studies. Moreover, it is to be apprehended that they might be insufficient for satisfactory understanding and modeling of many aspects beyond the large-scale circulation, e.g. the QBO. There is a need for improved understanding, in addition to more elaborate tuning, a research problem beyond the core tasks of NWP and climate research centers.

**Gravity wave distribution - Multiscale interactions:**

An interesting challenge with regard to progress in understanding and modeling of GW dynamics is its intrinsically multi-scale character. Interactions between GWs and synoptic-scale processes are involved as well as GW-GW interactions and GW-turbulence interactions. Likewise clouds and convective complexes leave their impact on GWs and are also influenced by them. Basis for improvements in understanding and modelling of GWs naturally would be a thorough diagnostics of all aspects of the GW distribution, spectrally, and in space and time. The inhomogeneous distribution and variability of GW source processes, GW propagation through and GW dissipation in various atmospheric layers lead to this GW distribution and its variability, as it is addressed today by numerous atmospheric measurements. Measurements are of fundamental importance for GW diagnostics. They provide the direct link to atmospheric reality. Individual measurements, however, are of selective nature. Every observation technique covers only a certain range of horizontal and vertical wavelengths. There are uncertainties in the measurement techniques and their evaluation methods to infer GWs. Measurements address only certain variables and are limited in the altitude range and geographical coverage. A synthesis of measurements in a consistent picture seems therefore needed. Such can be aided by a GW resolving atmosphere model. It would provide a synthetic laboratory within which to study GW generation, propagation and dissipation. Presently available GW permitting global models that follow the waves from the troposphere into the mesosphere, leave room, however, for further developments: They do not resolve the whole range of GW scales, they do not resolve all GW source processes, and they are not able to account for the dynamics and impact of non-hydrostatic waves, although these might be relevant for GW momentum transport. Non-hydrostatic models so far used for GW studies either have been applied in idealized numerical experiments or, if embedded into a NWP model, did not include the middle atmosphere. A non-hydrostatic global GW permitting model, at least locally able to resolve most GWs, seems to be still lacking. In order to address the complete life cycle of a GW spectrum, i.e. GW generation, propagation, and dissipation, such a model should extend from the ground into the lower thermosphere.

**Further Issues:**

Finally, the highly nonlinear nature of atmospheric dynamics critically limits the reproducibility of atmospheric measurements of the processes in question, as well as the control given to the scientist about the scenario to be examined. The process of spontaneous emission, however, seems accessible to regular laboratory experiments. Techniques to observe rotating stratified flows in the laboratory have significantly improved over the last decades. Due to improvements of hard- and software, non-invasive measurements can be performed with high accuracy. Measurements can be taken with high spatial and temporal resolution. The techniques are suited well to measure gravity waves in meridional and vertical cross sections.