Gravity Wave Drag Parameterization Research Articles

Response of a global atmospheric forecast model to various drag parametrizations

Various drag mechanisms are currently parametrized in numerical models of the atmosphere. For global models that include the middle atmosphere in particular, these mechanisms profoundly affect weather forecast as well as climate simulation.We have developed an extended-top version of the Navy Operational Global Atmospheric Prediction System (NOGAPS) to include the middle atmosphere by modifying some physical parametrizations and the vertical coordinate. We performed a series of ensemble simulations corresponding to January 2000 for investigating the response of the model to various drag mechanisms, such as mountain drag, orographic gravity wave drag, surface friction drag, and artificial model top drag. Based on the monthly mean fields obtained from the simulations, we first investigate the effect of gravity wave drag due to its direct impact through planetary wave activity as well as indirect impact through induced meridional circulation.We discuss the difficulties in partitioning between the mountain drag due to resolved orography and the gravity wave drag due to unresolved orography, first using conventional diagnostic measures. From analyses of the atmospheric angular momentum budget, we show that various model drag mechanisms when modified interact with one another by redistributing their drag while conserving the total amount. In particular, an overestimation of mountain drag is accompanied by an underestimation of gravity wave drag in the Northern Hemisphere mid-latitudes to conserve the total amount of drag in the model while likely breaking an optimal balance among the mechanisms. Under such a condition, the inclusion of a gravity wave drag parametrization — even if the drag amount itself is reasonable — does not necessarily improve the performance of the model. Diagnosis of this type of imbalance is not clear by conventional monthly mean fields of variables. In this paper, we argue that the budget of atmospheric angular momentum is a useful measure to diagnose impact of such changes in model physics with regard to the partition and balance among drag mechanisms. We also discuss the experimental results that led to the replacement of silhouette orography by mean orography in our model.

An overview of the past, present and future of gravity‐wave drag parametrization for numerical climate and weather prediction models

An overview of the parametrization of gravity ‐wave drag in numerical ‐weather prediction and climate simulation models is presented. The focus is primarily on understanding the current status of gravity wave drag parametrization as a step towards the new parametrizations that will be needed for the next generation of atmospheric models. Both the early history and latest developments in the field are discussed. Parametrizations developed specifically for orographic and convective sources of gravity waves are described separately, as are newer parametrizations that collectively treat a spectrum of gravity wave motions. The differences in issues in and approaches for the parametrization of the lower and upper atmospheres are highlighted. Various emerging issues are also discussed, such as explicitly resolved gravity waves and gravity wave drag in models, and a range of unparametrized gravity wave processes that may need attention for the next generation of gravity wave drag parametrizations in models.

An Accurate Spectral Nonorographic Gravity Wave Drag Parameterization for General Circulation Models

An accurate method of solution is developed for the Warner and McIntyre parameterization of nonorographic gravity wave drag for the case of hydrostatic dynamics in the absence of rotation. The new scheme is sufficiently fast that it is suitable for operational use in a general circulation model. Multiyear climate runs of the Canadian Middle Atmosphere Model are performed using the new scheme, and these are compared against equivalent climate runs using the full Warner and McIntyre scheme, which includes nonhydrostatic and rotational wave dynamics. The results indicate that the new operational scheme closely reproduces the seasonal distribution of time- and zonal-mean zonal winds, and the seasonal evolution of lower stratospheric temperatures that are obtained when the full Warner and McIntyre scheme is used. In addition, these quantities are shown to compare favorably with observations.

Simulation of the Baiu Front in a High Resolution AGCM.

The features of the Baiu front are examined using an AGCM with high resolution (T106L60). The Arakawa-Schubert scheme is used for the cumulus parameterization. The model clearly simulates the eastward-moving band of rain concentrated south of Japan during June, which can be considered the Baiu front. The characteristics of the Baiu front, such as the low level jet stream, a moist neutral stratification and a strong meridional gradient of moisture, are well simulated. Meso-α-scale disturbances appearing in the model are also comparable to the observational results. Experiments with varying horizontal resolutions keeping the same vertical resolution are also performed to examine resolution dependences. The distribution of precipitation is improved using higher resolution. In the T106L20 experiment, the Baiu-like frontal zone is formed by using a strong gravity wave drag parameterization. Thee strength of the subtropical jet is important over the Baiu front for a good simulation. Experiments with two different cumulus parameterizations (the moist convective adjustment, and Kuo schemes) are performed at T106L20 resolution to examine the effect of the parameterization on the simulation of the Baiu front. The moist convective adjustment scheme leads to high rainfall in the extra tropical region. The patterns of the Indian monsoon, and the North Pacific subtropical anticyclone, are quite different from those favorable to the formation of the Baiu front. On the other hand, a better distribution of precipitation is found using the Kuo scheme. However, an earlier disappearance of the Baiu front is seen in each cumulus parameterization experiment.

Simulations of fall and early winter in the stratosphere

Mechanistic model simulations of fall/early winter in the northern (November and December) and southern (May and June) stratosphere are compared with observational analyses to examine the skill of the model in simulating the state of the stratosphere, including both means and variability in key fields, during six winters. While detailed success varies from year to year, the model produces a realistic climatology of and variability in the evolution of winds, geopotential heights, temperatures and wave propagation in the early-winter stratosphere. The variability and mean fields agree well with those in longer data records. The northern hemisphere (NH) simulations show a small cold bias when averaged over the 6 years, while the southern hemisphere (SH) simulations show a larger warm bias. Greater detailed success in simulations of alternate NH winters suggests the possibility of greater model skill during the westerly quasi-biennial oscillation phase, although the short record and complexity of interactions between tropics and high latitudes preclude definitive identification of such a relationship. A prominent failing of the model when using Rayleigh friction to parametrize gravity-wave drag is an inability to correctly reproduce the latitudinal structure of the stratospheric jet above about 7 hPa; this failing can be alleviated by using a non-orographic gravity-wave drag parametrization, at the expense of frequently degrading agreement of planetary-wave phases and amplitudes. The success of the model in reproducing realistic climatology and variability makes these simulations useful for more detailed studies of transport and vortex evolution in early winter. Interhemispheric comparisons show that the early-winter circulations are qualitatively similar in the NH and SH: they are dominated by a strengthening vortex, with most wave activity being in wave 1; they both have minor warmings in a preferred location and clustered around a preferred time—early December (early June) in the NH (SH); variability in the flow shows a crescent pattern of maximum variations near 60–80° latitude centred at the location of the minor warmings (over the dateline in the NH and in the South Pacific in the SH). Interhemispheric differences are primarily in the magnitude of the variability, with a more symmetric circulation and weaker minor warmings in the SH; this is in contrast to later in the winter, when large qualitative interhemispheric differences have been seen. Copyright © 2002 Royal Meteorological Society

An Updated Parameterization of Convectively Forced Gravity Wave Drag for Use in Large-Scale Models

An updated parameterization of gravity wave drag forced by subgrid-scale cumulus convection (GWDC) in large-scale models is proposed. For an analytical formulation of the cloud-top wave stress, two-dimensional, steady-state, linear perturbations induced by diabatic heating are found in a two-layer structure with a piecewise constant shear with a critical level in the lower layer, a uniform flow in the upper layer, and piecewise constant buoyancy frequencies in each layer. The dynamical frame considered is relative to the diabatic forcing and the gravity waves obtained are stationary relative to the diabatic forcing, not necessarily stationary relative to the ground. The cloud-top wave momentum flux is proportional to the square of the magnitude of the convective heating, inversely proportional to the basic-state wind speed, and related to the buoyancy frequencies in each layer. The effect of wind shear in the convective region on the cloud-top momentum flux is negligible, while a difference in the stability between the two layers affects the momentum flux significantly. The cloud-top momentum flux increases as the stability in the convective region decreases and the stability above it increases. A global distribution of the 200-mb wave stress calculated using climatological data reveals that the wave stress in the present study is larger than that in a uniform wind and stability case. This is mainly due to the stability difference between the convective region and the region above it. A methodology of parameterizing GWDC in large-scale models using the wave saturation hypothesis is presented.

The Effect of Back-Reflection in the Parameterization of Non-Orographic Gravity-Wave Drag.

An efficient method of solution is developed for the Warner and McIntyre parameterization of the drag associated with nonhydrostatic non-orographic inertia-gravity waves. The scheme is sufficiently fast as to enable, for the first time, fully interactive multi-year climate simulations that include the effects of rotation and nonhydrostatic wave dynamics in the parameterization of non-orographic gravity wave drag. It is found that the new scheme alleviates much of the middle-atmosphere wind biases that occur in the Canadian Middle Atmosphere Model when either of its two operational hydrostatic non-orographic gravity wave drag parameterizations are used. The addition of the nonhydrostatic process of back-reflection has an important impact on the amount momentum flux launched into the stratosphere by the parameterization scheme. This quantity is a free parameter in the problem and it is specified here to be independent of time and geographic location. However, due to back-reflection, the net momentum flux that actually enters the stratosphere undergoes a systematic seasonal and latitudinal variation which is a consequence of the seasonal and latitudinal variation of the winds and temperatures in the middle atmosphere. This strong influence results in a characteristic latitudinal distribution for the net momentum flux entering the stratosphere in winter and summer. During these seasons, mid- to high-latitude launch momentum flux that is directed oppositely to the mesospheric jet can be reduced by as much as 75% due to back-reflection. The momentum flux launched into the stratosphere at tropical latitudes, however, is relatively unaffected by back-reflection. This has important implications for the forcing of tropical oscillations such as the semi-annual oscillation and the quasi-biennial oscillation in general circulation models.

The University of Illinois, Urbana‐Champaign three‐dimensional stratosphere‐troposphere general circulation model with interactive ozone photochemistry: Fifteen‐year control run climatology

A new University of Illinois at Urbana‐Champaign 24‐layer troposphere‐stratosphere general circulation model with interactive photochemistry is presented. We document here the results of a 15‐year‐long control run of the model and an evaluation of its performance. The ability of the model to simulate the Northern Hemisphere polar vortex has been improved because of the modification of the gravity wave drag parameterization. The extension and update of the chemical routine improved the simulated species distributions. As a result, the agreement of the simulated fields with observations is within 20% for total ozone and other species, 5 K for temperature, and 10 m s−1 for zonal wind over most of the atmosphere. The model simulates well the appearance of polar stratospheric clouds and the “ozone hole” over Antarctica. However, in some particular points the model results are unrealistic. These are (1) a cold bias (∼25 K) in the Southern Hemisphere lower stratosphere during austral summer, (2) a warm bias (∼20 K) in the middle stratosphere during austral winter, (3) a warm bias (∼10 K) near the stratopause in the tropics, and (4) a persistent cold bias of up to 8 K in the lowermost stratosphere almost everywhere over the globe. These problems may be due to the lack of a nonorographic gravity wave drag parameterization in the model, the influence of the top boundary conditions, and/or some problems with model treatment of the zonal wind‐planetary wave interaction in the stratosphere. Despite these few shortcomings, the model is now ready to be applied to several climate‐chemistry issues such as future ozone layer changes due to increasing greenhouse gas concentrations, the atmospheric influence of volcanic eruptions, and sun‐climate relations.

Numerical Simulations of Internal Gravity Wave Breaking in the Middle Atmosphere: The Influence of Dispersion and Three-Dimensionalization

Abstract A series of new analyses of the problem of the evolution of the internal gravity wave field that is excited when a uniformly stratified fluid flows over monochromatic topography is presented. Results demonstrate that upward-propagating waves overturn and break when they reach sufficient amplitude. The breaking of the wave field may occur due to either one or the other of two main effects, namely, the instability of the propagating wave front and the instability of the wave established behind the advancing front. The analysis of the wave–mean flow momentum transfer process reveals significant differences between these results and the predictions of two main gravity wave drag parameterization schemes (viz., those based upon so-called saturation theory and the spectral theory based on the critical layer absorption mechanism) regarding the dynamics of wave breaking and the spatial distribution of the resulting momentum transfer. The vertical extent and structure of the breaking region and, hence, the...

An investigation of boundary‐forcing sensitivities in a regional climate model

The sensitivity of a regional climate model to lateral, upper, and lower dynamical forcing is evaluated for a pan‐Arctic domain. The experiments focus on a month‐long case study of May 1990, but the results are shown to be extendable to January and July 1990. Although the control simulation is found to adequately represent major tropospheric circulation features, a large negative geopotential height bias of up to 700m is found at the upper levels of the model. Experiments find these biases are remedied through the replacement of a reflective rigid lid upper boundary condition with a local wave‐absorbing layer. Geopotential height biases are reduced to a maximum underestimation of only 50m at the upper boundary. Substantial improvement is also found in the simulated temperature and zonal wind profiles, transient heat and momentum fluxes, and stationary eddies as seen through the Eliassen‐Palm flux divergence. With this wave‐absorbing upper boundary condition in place, additional improvement is found using a gravity wave drag parameterization appropriate for this domain's 100km horizontal resolution. Additional sensitivity to lateral forcing is examined, and the relative role of the upper boundary condition to skillful simulations within the Arctic basin domain is discussed.

The Extended Canadian Middle Atmosphere Model

First results from the extended Canadian middle atmosphere model are presented. The model extends from the surface to the middle thermosphere and includes relevant physical parameterizations. To simulate unresolved gravity waves a non‐orographic gravity wave drag parameterization has also been implemented. Results from a two‐year simulation are discussed and are shown to be in good qualitative agreement with upper atmosphere research satellite wind observations. The realistic features which are reproduced include the reversal of the mesospheric jets and the semi‐annual variation of the migrating diurnal tide in the low latitude mesosphere.

Parameterization of gravity wave momentum deposition based on nonlinear wave interactions: basic formulation and sensitivity tests

We present a practical method for parameterization of gravity wave drag based on the Medvedev and Klaassen (1995. Journal of Geophysical Research 100, 25,841–25,853) theory of gravity wave spectral evolution and saturation. The only tuning necessary for the scheme involves assumptions about the nature of the source spectrum of subgrid-scale gravity waves, i.e. the wavenumbers, launch heights and amplitudes of the spectral components. In this paper we employ a column model with representative distributions of mean wind and temperature to examine the sensitivity of the parameterized wave drag to the source spectra. For the range of anticipated variability of source spectra in the troposphere the scheme produces plausible results consistent with observations and with theoretical estimates. Computationally, the scheme is as efficient as a multiple-wave Lindzen scheme, and suitable for use in general circulation models (GCMs) of the atmosphere.

Description and performance of the UIUC 24‐layer stratosphere/troposphere general circulation model

This paper describes the 24‐layer stratosphere/troposphere general circulation model (24‐L ST‐GCM) developed by the Climate Research Group of the University of Illinois at Urbana‐Champaign (UIUC). The model's dynamical and physical processes, similar to those of its ancestors, are briefly described. The newly implemented parameterizations of longwave and solar radiation, cloud‐radiation interaction, subgrid‐scale orographic gravity wave drag, and aerosol radiative forcing are described in more detail. Sensitivity tests using simplified one‐dimensional column models and the 24‐L ST‐GCM are carried out to evaluate these implementations. A 15‐year simulation with prescribed climatological sea‐surface temperatures and sea‐ice extents has been performed. To determine the model's strengths and weaknesses, the simulated results are compared with observations. The model simulates well the geographical distributions of surface‐air temperature and precipitation and their seasonal variations. The simulated cloud cover and cloud radiative forcing have the observed magnitudes and latitudinal variations, except near 60°S where the model underestimates the cloud cover by ∼20–30%. It is found that the large‐scale cloud distribution and the cloud‐top altitude depend on the respective critical relative humidities for the onset of large‐scale precipitation and penetrating convection. The model captures reasonably well the observed features of atmospheric temperature and zonal wind in both the stratosphere and troposphere in all seasons, with the exception of the northern stratospheric polar‐night jet. The simulated Transformed‐Eulerian‐Mean residual circulation in the stratosphere has comparable magnitudes and distributions to those obtained by data assimilation and other general circulation models (GCMs). The two‐cell Brewer‐Dobson circulation is captured. The use of an orographic‐type gravity wave drag parameterization is responsible for an abnormally warm northern polar stratosphere in winter, which is contrary to most other GCMs.

On the importance of gravity waves in the middle atmosphere and their parameterization in general circulation models

Abstract This tutorial paper discusses the problem of parameterizing unresolved gravity waves in general circulation models (GCMs) of the middle atmosphere. For readers who are unfamiliar with middle atmosphere dynamics a review of the basic dynamics of both the large-scale circulation and internal gravity waves is presented. A fairly detailed and physically-based description is given of several gravity wave drag (GWD) schemes that are currently employed in middle atmosphere GCMs. These include the parameterizations of McFarlane (1987) , Medvedev and Klaassen (1995) , and Hines, 1997a , Hines, 1997b , which are used in the Canadian Middle Atmosphere Model, as well as the parameterization of Fritts and Lu (1993) , which is used in the TIME-GCM. Results from a mechanistic model and the two above mentioned GCMs are presented and discussed. This paper is not intended as a review of all GWD parameterizations nor is it meant as a quantitative comparison of the schemes that have been chosen.

The Second-Generation Global Forecast System at the Central Weather Bureau in Taiwan

The global forecast system (GFS), which started its operation in 1988 at the Central Weather Bureau in Taiwan, has been upgraded to incorporate better numerical methods and more complete parameterization schemes. The second-generation GFS uses multivariate optimum interpolation analysis and incremental nonlinear normal-mode initialization to initialize the forecast model. The forecast model is a global primitive equation model with a resolution of 18 sigma levels in the vertical and 79 waves of triangular truncation in the horizontal. The forecast model includes a 1.5-order eddy mixing parameterization, a gravity wave drag parameterization, a shallow convection parameterization, a relaxed version of Arakawa–Schubert cumulus parameterization, grid-scale condensation calculation, and longwave and shortwave radiative transfer calculations with consideration of fractional clouds. The performance of the second-generation GFS is significantly better than the first-generation GFS. For two 3-month periods in winter 1995/96 and summer 1996, the second-generation GFS provided forecasters with 5-day forecasts where the averaged 500-mb height anomaly correlation coefficients for the Northern Hemisphere were greater than 0.6. Observational data available to the GFS are much less than those at other numerical weather prediction centers, especially in the Tropics and Southern Hemisphere. The GRID messages of 5° resolution, ECMWF 24-h forecast 500-mb height and 850- and 200-mb wind fields available once a day on the Global Telecommunications System are used as supplemental observations to increase the data coverage for the GFS data assimilation. The supplemental data improve the GFS performance both in the analysis and forecast.

The Second–Generation Global Forecast System at the Central Weather Bureau in Taiwan

Abstract The global forecast system (GFS), which started its operation in 1988 at the Central Weather Bureau in Taiwan, has been upgraded to incorporate better numerical methods and more complete parameterization schemes. The second-generation GFS uses multivariate optimum interpolation analysis and incremental nonlinear normal-mode initialization to initialize the forecast model. The forecast model is a global primitive equation model with a resolution of 18 sigma levels in the vertical and 79 waves of triangular truncation in the horizontal. The forecast model includes a 1.5-order eddy mixing parameterization, a gravity wave drag parameterization, a shallow convection parameterization, a relaxed version of Arakawa–Schubert cumulus parameterization, grid-scale condensation calculation, and longwave and shortwave radiative transfer calculations with consideration of fractional clouds. The performance of the second-generation GFS is significantly better than the first-generation GFS. For two 3-month periods in winter 1995/96 and summer 1996, the second-generation GFS provided forecasters with 5-day forecasts where the averaged 500-mb height anomaly correlation coefficients for the Northern Hemisphere were greater than 0.6. Observational data available to the GFS are much less than those at other numerical weather prediction centers, especially in the Tropics and Southern Hemisphere. The GRID messages of 5° resolution, ECMWF 24-h forecast 500-mb height and 850- and 200-mb wind fields available once a day on the Global Telecommunications System are used as supplemental observations to increase the data coverage for the GFS data assimilation. The supplemental data improve the GFS performance both in the analysis and forecast.

A Very High Resolution General Circulation Model Simulation of the Global Circulation in Austral Winter

This paper discusses a simulation obtained with the Geophysical Fluid Dynamics Laboratory “SKYHI” troposphere–stratosphere–mesosphere general circulation model run at very high horizontal resolution (∼60-km grid spacing) and without any parameterization of subgrid-scale gravity wave drag. The results are for a period around the austral winter solstice, and the emphasis is on the simulated Southern Hemisphere (SH) winter circulation. Comparisons are made with results obtained from lower horizontal resolution versions of the same model. The focus in this paper is on two particularly striking features of the high-resolution simulation: the extratropical surface winds and the winter polar middle atmospheric vortex. In the extratropical SH, the simulated surface westerlies and meridional surface pressure gradients in the high-resolution model are considerably stronger than observed and are stronger than those simulated at lower horizontal resolution. In the middle atmosphere, the high-resolution model produces a simulation of the zonal mean winter polar vortex that is considerably improved over that found with lower resolution models (although it is still significantly affected by the usual cold pole bias). Neither the improvement of the middle atmospheric polar vortex simulation nor the deterioration of the simulation of surface winds with increased model resolution shows a clear convergence, even at the ∼60-km grid spacing employed here.

A NOTE ON THE APPLICATION OF LINEAR WAVE THEORY AT A CRITICAL LEVEL

The purpose of this note is to estimate the accuracy and practical limitations of applying linear theory at a critical level over a realistic range of atmospheric stabilities for an idealized surface terrain. These estimates are made by comparing the results of a linear model with a nonlinear numerical model at a critical level. Essentially similar results are obtained from each model for wave stress, wave breaking height and wave dissipation through the critical level. Because gravity waves can be either evanescent or internal depending on the relative sizes of the Scorer parameter and the wavenumber of the ground surface disturbance, the somewhat paradoxical result develops that wave breaking and non-linearity increase with increasing bulk Richardson number. It is recommended that steady linear wave theory be used in gravity wave drag parameterizations provided near real time profiles of background velocity and temperature are available.

Seasonal variation of middle atmospheric CH4 and H2O with a new chemical‐dynamical model

A new zonally averaged, chemical‐dynamical model of the middle atmosphere is used to study the processes which control the distributions and seasonal variability of CH4 and H2O. This model incorporates a nondiffusive, nondispersive advection scheme, a time‐dependent linear model of planetary wave drag and horizontal mixing (Kyy), a new parameterization of gravity wave drag and vertical mixing (Kzz), and an explicit treatment of LTE (local thermodynamic equilibrium) and non‐LTE IR cooling. Model chemistry is calculated using a Newton‐Raphson iterative scheme, which allows consistent simulations of species with highly nonuniform chemical lifetimes. In this study we focus on the sensitivity of model CH4 and H2O to the magnitude of tropospheric latent heat release, planetary wave and gravity wave activity, and the methane oxidation rate. Model results show that in the tropical stratosphere their vertical distributions are strong functions of both the methane oxidation rate and the ascent rate, the latter driven by a combination of tropospheric latent heat release and atmospheric drag. At low latitudes HALOE observations and model results both show conservation of “potential H2” (2×CH4+H2O) below ∼50 km. However, the conservation of potential H2 from HALOE observations breaks down above ∼55 km, while the model shows conservation well into the middle mesosphere (∼70 km). This may suggest serious inadequacies in our understanding of the photochemistry of water vapor and mesospheric HOx, in particular those processes which control the partitioning of H2 and H2O. At high latitudes, H2O model/data comparisons suggest that horizontal mixing is important in determining the observed latitudinal gradient in mesospheric water vapor. We also find that inside the polar winter vortex, while the strength of tropical latent heat forcing and planetary wave drag influence the descent rate, both horizontal mixing and the methane photochemistry play important roles in determining the CH4 mixing ratio. Finally, we suggest that the observed interhemispheric asymmetry in the seasonal cycle of mesospheric H2O may be linked to larger values of Kzz in the southern winter mesosphere. This represents a key difference between mesospheric and stratospheric tracer transport. In the stratosphere, greater net unmixed descent in the southern hemisphere directly translates into lower tracer values relative to the northern hemisphere, while mesospheric tracer transport shows the opposite behavior.

Parameterization of gravity wave drag in comprehensive models of the middle atmosphere

Within the past decade gravity wave parameterization has come into widespread use in atmospheric general circulation models (GCMs). Most of the schemes used hitherto are based on a simplified linear representation of the gravity waves. Advances in theoretical understanding of gravity wave processes in the middle atmosphere have been achieved in recent years largely as a result of the observational work of the past decade. These advances have in turn led to new parameterization proposals. This paper reviews briefly the state of gravity wave parameterization as used in GCMs and presents selected results from an application of a new scheme — the Doppler Spread Parameterization proposed by Hines (1996a,b)