Seeking New Quantitative Constraints on Orographic Gravity Wave Stress and Drag to Satisfy Emerging Needs in Seasonal-to-Subseasonal and Climate Prediction: An Update from the SPARC Gravity Wave Activity
M. Joan Alexander, Julio Bacmeister, Manfred Ern, Sonja Gisinger, Lars Hoffmann, Laura Holt, Christopher Kruse, Riwal Plougonven, Inna Polichtchouk, Petr Sacha, Kaoru Sato, Ryosuke Shibuya, Annelize van Niekerk, and Corwin Wright
Orographic gravity wave (OGW) drag is one of the fundamental physics parametrizations employed in every global numerical model across timescales from weather to climate. Orographic waves are part of the complex dynamical interaction of winds with topography, and one piece in that puzzle is topography's effect on global circulation. Parametrized OGW drag provides an important control on model wind biases at levels from the surface through to the middle atmosphere, and these alterations in winds in turn affect stationary and synoptic Rossby wave propagation and dissipation. Thus, properly tuned OGW drag parameterizations can improve weather model prediction skill from synoptic to seasonal timescales (Palmer et al. 1986; Lott and Miller 1997; Charron et al. 2012; Sigmond et al. 2013; Shaw et al. 2014). Climate models have long relied on OGW drag parameterizations for improved representations of both the mean climate and variability (Alexander et al. 2010). In the stratosphere in particular, the circulation changes associated with OGW drag reduce winter temperature biases that affect ozone chemistry, so OGW drag is also fundamental to chemistry-climate modeling (Eyring et al. 2010).
Despite its importance in global models, OGW parametrization tuning is still only weakly constrained by observations in today's models, while new issues related to shortcomings in OGW parametrization are arising. OGW parameterizations have been employed in global models for over 30 years, yet new parameterization methods are still being developed (e.g. Bacmeister et al. 2019). Unlike some atmospheric processes that are fully unresolved across most atmospheric model resolutions, such as microphysics or turbulence, larger-scale mountain waves can be partly resolved by the model dynamics, while sub-grid effects of smaller-scale waves must be parametrized. Modern orographic drag parametrizations attempt to be 'scale-aware' by reducing their sub-grid variance and OGW horizontal scale with increasing resolution (e.g. Polichtchouk et al. 2018).
Are these the newer parameterizations and scale-aware changes tunings more realistic? Evaluations are generally based on zonal-mean wind changes or global forecast skill scores, but these do not tell the whole story. Such parameterization changes also affect global distributions of drag in models and therefore regional and seasonal circulation patterns in the stratosphere and troposphere (Polichtchouk et al. 2018a,b). In a new project jointly supported by SPARC and the International Space Science Institute (ISSI), the SPARC Gravity Wave Activity began a new focus on using satellite observations to constrain OGW drag in global models.
The interaction of winds with mountainous terrain leads to both drag forces in the boundary layer as well as exchanges of momentum between the surface and the overlying atmosphere. Part of the momentum is carried vertically by OGWs, which grow in amplitude exponentially with height to conserve energy, and somewhere aloft, the waves break or dissipate. This exerts forces on the flow we call OGW drag. The key variable in this momentum exchange is the wave stress (or momentum flux). These OGW stresses and forces can be locally quite large with important nonlinear circulation effects (Cohen et al. 2013; Sacha et al. 2016; Sato and Nomoto 2015; Sato et al. 2018). Observing the stress directly requires observation of 3D wind anomalies (u',v',w'), which are historically difficult to measure from space, particularly for the vertical wind, which can be orders of magnitude smaller than horizontal wind. Ern et al. (2004) related the stress to the more directly measured wave temperature anomalies, which requires measurement of the local 3D wave properties: horizontal wavenumber vector, vertical wavenumber, and wave amplitude. OGW with horizontal wavelengths as short as ∼20 km are important (Smith et al. 2016), so the satellite measurements must have very high resolution. Earlier attempts with limb-viewing satellite measurements from CRISTA, HIRDLS, SABER, and MLS provided only 2D measures of an apparent horizontal wavenumber and crude measures of stress magnitude. A 2010 SPARC/ISSI team found these 2D limb-viewing estimates to not only be low-biased, as expected, but also highly uncertain depending on the analysis method (Geller et al. 2013).
Specialized high-resolution stratospheric temperature retrievals from hyper-spectral infrared nadir sounding instruments with cross-orbital scan patterns like the Atmospheric Infrared Sounder (AIRS) and the Infrared Atmospheric Sounding Interferometer (IASI) can provide the necessary information on the 3D structure of OGW (Hoffmann and Alexander 2009), and advanced wave analysis methods have been developed for computing global gravity stresses (Ern et al. 2017; Wright et al. 2017; Hindley et al. 2019). However, uncertainty in these methods is still difficult to quantify. The observations have many additional limitations including horizontal and vertical resolution limits and limitation to stratospheric levels only (Figure 1). What is more, while OGW stresses may be computed directly from the observations, the drag forces cannot be observed due to observational filter effects (Alexander and Sato 2015).
Figure 1: Gravity wave temperature anomalies from AIRS high-resolution stratospheric temperature retrievals [Hoffmann and Alexander 2009], showing the 3d structure of orographic waves over the Southern Andes. Figure from Wright et al. 2017.
In addition to uncertainties in the observations, there remain important uncertainties also in high-resolution model representations of gravity waves. Issues include model resolution (both horizontal and vertical), numerical scheme and implicit numerical dissipation, explicit scale-dependent dissipation, parameterization of moist processes, surface topography and boundary layer specifications, and partitioning of parametrized gravity wave drag between orographic and nonorographic sources (Polichtchouk et al. 2018b). Studies also suggest that simple-minded scale-aware parameterizations that scale with model resolution do not result in consistent representation of OGW drag across resolutions (van Niekerk et al. 2016) and that resolved waves are strongly influenced by boundary layer treatments.
In a first meeting 1-5 April 2019, our team of 13 experts in OGW observations, drag parameterizations, and global and regional modeling assembled at ISSI in Bern, Switzerland to discuss how best to use the global observations, despite their limitations, to provide new constraints on the problem of OGW drag. In addition to the evaluation of uncertainties in available observations, discussions also focused on OGW drag parameterizations and high-resolution modeling.
Discussion on Parametrization Limitations
Current state-of-the-art OGW drag parametrizations make several simplifying assumptions, a few of which were discussed as being of a particular importance: i) instant vertical propagation of monochromatic waves, ii) lack of horizontal wave propagation, and iii) saturation assumptions for wave dissipation with height. Observational and high-resolution modeling results indicate that OGWs can be located far from their source region (e.g., Ehard et al. 2017), emphasizing the need to revisit these assumptions. Importance of advection and refraction of GWs by the background flow, and, the dependence of the vertical group velocity on the horizontal wavenumber was stressed by several working group members (Sato et al. 2012; Kruse & Smith 2018; Shibuya & Sato 2019). Therefore, relaxing these simplifying assumptions implies that the spatial distribution and the partitioning of OGW drag between zonal and meridional components will change (e.g., Amemiya & Sato, 2016). OGW reflection from the tropopause and heating by OGW drag was discussed as being potentially important for the circulation.
Discussion on Scale-aware Parametrizations
Several talks highlighted the fact that the behavior of orographic waves and the drag that they impart on the atmosphere depends on their horizontal scale (Smith and Kruse 2018), such that the relative importance of representing certain processes in parametrizations varies across resolutions. For example, the vertical phase velocity of the mountain waves is proportional to their horizontal wave number. This means that, as the model horizontal resolution decreases and more of the waves become unresolved, the assumption of instantaneous propagation, a common approximation amongst OGWD parametrizations, becomes more severe. If the model's vertical resolution is too coarse, the vertical variations of the OGW may then also be sub-grid, which is an aspect not currently well represented by parametrizations. In fact, a series of gravity-wave permitting model experiments indicate that simulated gravity wave stresses highly depend on the vertical resolution (Watanabe et al. 2015). It became evident that we do not have a good understanding of how the stress should increase or decrease with increasing vertical resolution and, as a result, how the parametrizations should account for this.
Understanding the scales (in both the vertical and horizontal) that are contributing to the OGW stresses and drag, and their horizontal as well as vertical distributions, therefore, seems to be paramount to developing improved scale-aware parametrizations. This motivates the need for a more detailed description of the global statistics of the wave fields from observations and models, so that we may judge the importance of different aspects of waves and their propagation in the real atmosphere. Namely, the horizontal and vertical wavelengths and propagation directions of the waves, as well as their geographic distribution and magnitudes and dependence on the background winds, may help to inform the development of scale-aware parametrizations.
Discussion on Global High-resolution Data Assimilation/Forecast Tools
Output from high-resolution data assimilation systems and forecast models contain many realistic signatures of gravity waves (Preusse et al. 2014; Hoffmann et al. 2017; Holt et al. 2017). However, even at resolutions < 10 km, only a portion of the gravity wave spectrum is resolved. So these model systems are best described as gravity wave 'permitting' rather than 'resolving'. One major advantage of data assimilation is that large-scale wind and temperature are well-constrained by observations, so smaller-scale waves propagate in realistic conditions (Gisinger et al. 2017). For OGW, where surface topography defines the wave sources, this can potentially yield highly realistic simulation of OGW (Figure 2). However, topographic smoothing and various forms of dissipation from the boundary layer to the stratosphere may conspire to give poor comparisons between simulated OGW and observations despite sufficient resolution. Combining different types of observations at different levels, e.g. satellite, radar, lidar, and balloon measurements, permits a more complete evaluation of all the scales of waves simulated.
Figure 2: Brightness temperature anomalies from (left) AIRS and (right) MERRA-2 12.5-km Replay for January 13, 2007.
Discussion on Comparing Models and Observations
Before using observations to validate models, we first need to evaluate uncertainties in those observations and carefully consider which parts of the wave spectrum are included/excluded. Waves are always first isolated as perturbations on some larger-scale background value, and the method for defining the background needs to be considered carefully in any comparison. Comparing waves in satellite observations and models is best accomplished by sampling the models with the satellite sampling pattern and kernel functions or by applying a radiative transfer model to simulate satellite observations for direct comparison.
Some important issues discussed include: (a) Are line-of-sight slant paths important, or can they be neglected to first order? (b) What model resolution is sufficient for the comparison to the observations? Issues include model numerical scheme and implicit and explicit dissipation at small scales. (c) How representative are case studies to the global problem? If regional comparisons are planned, the locations and times will depend on availability of other observations besides the satellite data. Will these locations/times permit characterization of important OGW properties globally? (d) How important is it to include non-hydrostatic waves? This is an issue for comparisons to global gravity wave permitting models. (e) How do we best to evaluate model/observation differences (e.g. strength versus shifts in location). (f) Can we use observations to determine the relative importance of different scales of waves? (g) Can observations help to constrain compensation between Rossby waves and gravity waves that is observed in models? (h) If we only have stratospheric wave observations, can these help with tropospheric factors in OGW parameterizations? (i) Are there significant differences in OGW stress in models with different dynamical cores due to the different methods in calculating the stress, or can intermodel differences be understood solely in terms of implicit/explicit dissipation?
Discussion on Intercomparison of Satellite-based OGW Stresses
Different methods used for satellite analysis appear to give quite different gravity wave stress results, both for individual cases and global means. Methods agree well qualitatively, but closer quantitative comparisons reveal significant differences. Considerations that are not commonly discussed in the literature include important differences between conditional versus unconditional mean stresses. Analogous to other intermittent phenomena like precipitation, the mean values and global patterns in gravity waves can be significantly different for conditional and unconditional averages. This likely contributed to differences among observations reported by Geller et al (2013). The intermittent nature of gravity waves also leads to the question of how best to report on their global properties. For example, distributions in gravity wave amplitudes show that infrequent values, 10-100 times larger than the mean, contribute most of the mean stress (Hertzog et al. 2012; de la Camara and Lott 2015). Directional stresses are another important issue that require more attention. Particularly for global observations that will include both OGWs and waves from moving sources like convection, averaging may obscure important directional stresses with cancellation of positive and negative values across different wave events. One goal may be to formulate, as a group, general recommendations for how gravity wave activity should be reported, both for observational and modeling studies.
Focused Research Questions
The team defined a set of focused research questions to jointly address:
- How well do methods used for computing gravity wave stress from satellite temperatures represent the true stress derived from 3-dimensional winds?
- How well does satellite-computed stress compare between different analysis methods?
- How well do different high-resolution, limited-area models reproduce satellite and other observations of OGW?
- How can we use answers to 1-3 to improve parameterization of OGW drag in coarser-resolution global forecasting models?
Observing System Simulation Experiments (OSSE) for gravity waves
In order to address these questions, the team has planned a set of regional simulations to address questions 1 through 3. In the spirit of the OSSE, the simulations are designed for the AIRS and IASI satellite sampling and kernel functions in order to create a simulated set of satellite observations of OGWs. Different wave analysis methods will be applied to these simulated satellite data from model temperatures and resulting wave stresses can be compared to those calculated from simulated winds (u',v',w') for evaluation of the analysis method uncertainties (Q1). This also affords a direct comparison of the different analysis methods (Q2). European Centre for Medium-Range Weather Forecasting (ECMWF) or Modern-Era Retrospective analysis for Research and Applications (MERRA-2) analyses will serve as initial and boundary conditions for the OSSE, so we can also compare the simulated satellite observations to the real satellite observations on the same days/times in order to validate the realism of the simulations (Q3). The simulation locations and dates have further been chosen to permit comparison of simulated gravity waves to other observational datasets in order to validate portions of the simulated gravity wave spectrum that are not visible in the satellite data (Q3). As a first step towards answering Q4, the high-resolution simulations and validating observations will also be compared to parameterizations of OGW drag in coarser resolution global models, with the expectation that this will either validate the parameterizations or suggest new tuning parameters or appropriate modifications to the parameterization methods. While portions of these research tasks have been performed previously by individual research groups, we hope our coordinated international collaboration will provide new and meaningful constraints for global prediction models.
The first set of simulations targets the Southern Andes and Antarctic Peninsula region (Figure 3) during October 2010, when super-pressure balloon observations of gravity waves are available through the Concordiasi field campaign (Jewtoukoff et al. 2015). These data observe the full spectrum of gravity waves from the inertial frequency to the buoyancy frequency at levels in the lower stratosphere. Measurements from radiosondes and radio-occultation are also available. Additional foci are planned for Scandinavia, New Zealand, and Syowa Station Antarctica.
Within the limits of the model resolutions, the validated simulations can also be used to study other aspects of the interaction between the atmosphere and complex surface topography at levels from the surface through the stratosphere. These include surface stress, form drag, turbulence, and other nonlinearities. Once the simulations are carefully validated against observations as described above, additional studies to examine these aspects of the simulations are planned. The OGW OSSE datasets will be made publicly available for any further studies by the scientific community. We hope these further studies will provide natural links to a parallel project on Surface Drag and Momentum Transport that is sponsored by GEWEX/GASS. A joint workshop on orographic stress and drag from the surface to the middle atmosphere (Sandu et al. 2019) with participation from these two projects and an open invitation to the broader community may be planned for late 2020.
Figure 3: (a) Regional domain for the first OSSE experiment; (b) Coverage of Concordiasi super-pressure balloon tracks (orange) during the OSSE period 9-19 October 2010.
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Our first meeting will provisionally be at ISSI Bern in April 2019. Watch this space for more details as the date approaches!