Efficient Modeling of the Interaction of Mesoscale Gravity Waves with Unbalanced Large-Scale Flows: Pseudomomentum-Flux Convergence versus Direct Approach

Abstract

This paper compares two different approaches for the efficient modeling of subgrid-scale inertia–gravity waves in a rotating compressible atmosphere. The first approach, denoted as the pseudomomentum scheme, exploits the fact that in a Lagrangian-mean reference frame the response of a large-scale flow can only be due to forcing momentum. Present-day gravity wave parameterizations follow this route. They do so, however, in an Eulerian-mean formulation. Transformation to that reference frame leads, under certain assumptions, to pseudomomentum-flux convergence by which the momentum is to be forced. It can be shown that this approach is justified if the large-scale flow is in geostrophic and hydrostatic balance. Otherwise, elastic and thermal effects might be lost. In the second approach, called the direct scheme and not relying on such assumptions, the large-scale flow is forced both in the momentum equation, by anelastic momentum-flux convergence and an additional elastic term, and in the entropy equation, via entropy-flux convergence. A budget analysis based on one-dimensional wave packets suggests that the comparison between the abovementioned two schemes should be sensitive to the following two parameters: 1) the intrinsic frequency and 2) the wave packet scale. The smaller the intrinsic frequency is, the greater their differences are. More importantly, with high-resolution wave-resolving simulations as a reference, this study shows conclusive evidence that the direct scheme is more reliable than the pseudomomentum scheme, regardless of whether one-dimensional or two-dimensional wave packets are considered. In addition, sensitivity experiments are performed to further investigate the relative importance of each term in the direct scheme, as well as the wave–mean flow interactions during the wave propagation.

Toward Transient Subgrid-Scale Gravity Wave Representation in Atmospheric Models. Part I: Propagation Model Including Nondissipative Wave–Mean-Flow Interactions

“…The latter would enter via their horizontal convergence, which one is inclined to avoid in singlecolumn GWPs. Wei et al (2019) discussed this approximation in detail. Equation ( 6) basically assumes that the large-scale flow is in geostrophic and hydrostatic balance.…”

“…Another drawback of GWPs in current climate and weather codes is that their applicability outside of the tropics (where Coriolis effects are nonnegligible) relies on the assumption of balanced (hydrostatic, geostrophic) resolved flows, which might not be valid with the increasing spatial resolutions applied nowadays. If, however, the resolved flow is not balanced, additional forcing terms due to the GW dynamics appear both in the momentum and the entropy equation representing, for example, elastic effects (Achatz et al 2017;Wei et al 2019). Potential triad wave-wave interactions in the atmosphere are also not taken into account in current GWPs, although their neglect has never been justified explicitly, to the best of our knowledge.…”

How does knowledge of atmospheric gravity waves guide their parameterizations?

“…With regard to lateral propagation and secondary generation, sufficient evidence from observations and modelling has been accumulated to motivate a revisit to the common framework of gravity wave parameterizations. This has already been undertaken in the coordinated German Research Foundation's research unit on Multiscale Dynamics of Gravity Waves (MS‐Gwaves), which combines theoretical, numerical and observational efforts (e.g., Bölöni et al ., ; Wei et al ., ).…”

Magnitudes of Gravity Wave Pseudomomentum Flux Derived by Combining COSMIC Radio Occultation and ERA-Interim Reanalysis Data

“…What needs to be pointed out is that in many previous studies, the two concepts, MF and the vertical flux of horizontal pseudomomentum, or simply pseudomomentum flux (PMF), are treated the same. While according to the discussion in Wei et al [33], the mathematical expressions of the two concepts are not the same, and their magnitudes can be different, especially for inertia-gravity waves. Compared with MF, all horizontal flux gradients are neglected in PMF and no elastic or heating effect by GWs are included, and the gravity wave parameterization scheme in the current generation of the operational climate models is based on the PMF convergence.…”