Search Results
Abstract
Quantification of inertia–gravity waves (IGWs) generated by upper-level jet–surface front systems and their parameterization in global models of the atmosphere relies on suitable methods to estimate the strength of IGWs. A harmonic divergence analysis (HDA) that has been previously employed for quantification of IGWs combines wave properties from linear dynamics with a sophisticated statistical analysis to provide such estimates. A question of fundamental importance that arises is how the measures of IGW activity provided by the HDA are related to the measures coming from the wave–vortex decomposition (WVD) methods. The question is addressed by employing the nonlinear balance relations of the first-order δ–γ, the Bolin–Charney, and the first- to third-order Rossby number expansion to carry out WVD. The global kinetic energy of IGWs given by the HDA and WVD are compared in numerical simulations of moist baroclinic waves by the Weather Research and Forecasting (WRF) Model in a channel on the f plane. The estimates of the HDA are found to be 2–3 times smaller than those of the optimal WVD. This is in part due to the absence of a well-defined scale separation between the waves and vortical flows, the IGW estimates by the HDA capturing only the dominant wave packets and with limited scales. It is also shown that the difference between the HDA and WVD estimates is related to the width of the IGW spectrum.
Abstract
Quantification of inertia–gravity waves (IGWs) generated by upper-level jet–surface front systems and their parameterization in global models of the atmosphere relies on suitable methods to estimate the strength of IGWs. A harmonic divergence analysis (HDA) that has been previously employed for quantification of IGWs combines wave properties from linear dynamics with a sophisticated statistical analysis to provide such estimates. A question of fundamental importance that arises is how the measures of IGW activity provided by the HDA are related to the measures coming from the wave–vortex decomposition (WVD) methods. The question is addressed by employing the nonlinear balance relations of the first-order δ–γ, the Bolin–Charney, and the first- to third-order Rossby number expansion to carry out WVD. The global kinetic energy of IGWs given by the HDA and WVD are compared in numerical simulations of moist baroclinic waves by the Weather Research and Forecasting (WRF) Model in a channel on the f plane. The estimates of the HDA are found to be 2–3 times smaller than those of the optimal WVD. This is in part due to the absence of a well-defined scale separation between the waves and vortical flows, the IGW estimates by the HDA capturing only the dominant wave packets and with limited scales. It is also shown that the difference between the HDA and WVD estimates is related to the width of the IGW spectrum.
Abstract
Machine learning (ML) provides a powerful tool for investigating the relationship between the large-scale flow and unresolved processes, which need to be parameterized in climate models. The current work explores the performance of the random forest regressor (RF) as a nonparametric model in the reconstruction of nonorographic gravity waves (GWs) over midlatitude oceanic areas. The ERA5 dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF) model outputs is employed in its full resolution to derive GW variations in the lower stratosphere. Coarse-grained variables in a column-based configuration of the atmosphere are used to reconstruct the GWs variability at the target level. The first important outcome is the relative success in reconstructing the GW signal (coefficient of determination R2 ≈ 0.85 for “E3” combination). The second outcome is that the most informative explanatory variable is the local background wind speed. This questions the traditional framework of gravity wave parameterizations, for which, at these heights, one would expect more sensitivity to sources below than to local flow. Finally, to test the efficiency of a relatively simple, parametric statistical model, the efficiency of linear regression was compared to that of random forests with a restricted set of only five explanatory variables. Results were poor. Increasing the number of input variables to 15 hardly changes the performance of the linear regression (R2 changes slightly from 0.18 to 0.21), while it leads to better results with the random forests (R2 increases from 0.29 to 0.37).
Abstract
Machine learning (ML) provides a powerful tool for investigating the relationship between the large-scale flow and unresolved processes, which need to be parameterized in climate models. The current work explores the performance of the random forest regressor (RF) as a nonparametric model in the reconstruction of nonorographic gravity waves (GWs) over midlatitude oceanic areas. The ERA5 dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF) model outputs is employed in its full resolution to derive GW variations in the lower stratosphere. Coarse-grained variables in a column-based configuration of the atmosphere are used to reconstruct the GWs variability at the target level. The first important outcome is the relative success in reconstructing the GW signal (coefficient of determination R2 ≈ 0.85 for “E3” combination). The second outcome is that the most informative explanatory variable is the local background wind speed. This questions the traditional framework of gravity wave parameterizations, for which, at these heights, one would expect more sensitivity to sources below than to local flow. Finally, to test the efficiency of a relatively simple, parametric statistical model, the efficiency of linear regression was compared to that of random forests with a restricted set of only five explanatory variables. Results were poor. Increasing the number of input variables to 15 hardly changes the performance of the linear regression (R2 changes slightly from 0.18 to 0.21), while it leads to better results with the random forests (R2 increases from 0.29 to 0.37).
Abstract
The parameterization of inertia–gravity waves (IGWs) is of considerable importance in general circulation models. Among the challenging issues faced in studies concerned with parameterization of IGWs is the estimation of diabatic forcing in a way independent of the physics parameterization schemes, in particular, convection. The requirement is to estimate the diabatic heating associated with balanced motion. This can be done by comparing estimates of balanced vertical motion with and without diabatic effects. The omega equation provides the natural method of estimating balanced vertical motion without diabatic effects, and several methods for including diabatic effects are compared. To this end, the assumption of spatial-scale separation between IGWs and balanced flows is combined with a suitable form of the balanced omega equation. To test the methods constructed for estimating diabatic heating, an idealized numerical simulation of the moist baroclinic waves is performed using the Weather Research and Forecasting (WRF) Model in a channel on the f plane. In overall agreement with the diabatic heating of the WRF Model, in the omega-equation-based estimates, the maxima of heating appear in the warm sector of the baroclinic wave and in the exit region of the upper-level jet. The omega-equation-based method with spatial smoothing for estimating balanced vertical motion is thus presented as the proper way to evaluate diabatic forcing for parameterization of IGWs.
Abstract
The parameterization of inertia–gravity waves (IGWs) is of considerable importance in general circulation models. Among the challenging issues faced in studies concerned with parameterization of IGWs is the estimation of diabatic forcing in a way independent of the physics parameterization schemes, in particular, convection. The requirement is to estimate the diabatic heating associated with balanced motion. This can be done by comparing estimates of balanced vertical motion with and without diabatic effects. The omega equation provides the natural method of estimating balanced vertical motion without diabatic effects, and several methods for including diabatic effects are compared. To this end, the assumption of spatial-scale separation between IGWs and balanced flows is combined with a suitable form of the balanced omega equation. To test the methods constructed for estimating diabatic heating, an idealized numerical simulation of the moist baroclinic waves is performed using the Weather Research and Forecasting (WRF) Model in a channel on the f plane. In overall agreement with the diabatic heating of the WRF Model, in the omega-equation-based estimates, the maxima of heating appear in the warm sector of the baroclinic wave and in the exit region of the upper-level jet. The omega-equation-based method with spatial smoothing for estimating balanced vertical motion is thus presented as the proper way to evaluate diabatic forcing for parameterization of IGWs.
Abstract
The way the large-scale flow determines the energy of the nonorographic mesoscale inertia–gravity waves (IGWs) is theoretically significant and practically useful for source parameterization of IGWs. The relations previously developed on the f plane for tropospheric sources of IGWs including jets, fronts, and convection in terms of associated secondary circulations strength are generalized for application over the globe. A low-pass spatial filter with a cutoff zonal wavenumber of 22 is applied to separate the large-scale flow from the IGWs using the ERA5 data of ECMWF for the period 2016–19. A comparison with GRACILE data based on satellite observations of the middle stratosphere shows reasonable representation of IGWs in the ERA5 data despite underestimates by a factor of smaller than 3. The sum of the energies, which are mass-weighted integrals in the troposphere from the surface to 100 hPa, as given by the generalized relations is termed initial parameterized energy. The corresponding energy integral for the IGWs is termed the diagnosed energy. The connection between the parameterized and diagnosed IGW energies is explored with regression analysis for each season and six oceanic domains distributed over the globe covering the Northern and Southern Hemispheres and the tropics. While capturing the seasonal cycle, the domain area-average seasonal mean initial parameterized energy is weaker than the diagnosed energy by a factor of 3. The best performance in regression analysis is obtained by using a combination of power and exponential functions, which suggests evidence of exponential weakness.
Abstract
The way the large-scale flow determines the energy of the nonorographic mesoscale inertia–gravity waves (IGWs) is theoretically significant and practically useful for source parameterization of IGWs. The relations previously developed on the f plane for tropospheric sources of IGWs including jets, fronts, and convection in terms of associated secondary circulations strength are generalized for application over the globe. A low-pass spatial filter with a cutoff zonal wavenumber of 22 is applied to separate the large-scale flow from the IGWs using the ERA5 data of ECMWF for the period 2016–19. A comparison with GRACILE data based on satellite observations of the middle stratosphere shows reasonable representation of IGWs in the ERA5 data despite underestimates by a factor of smaller than 3. The sum of the energies, which are mass-weighted integrals in the troposphere from the surface to 100 hPa, as given by the generalized relations is termed initial parameterized energy. The corresponding energy integral for the IGWs is termed the diagnosed energy. The connection between the parameterized and diagnosed IGW energies is explored with regression analysis for each season and six oceanic domains distributed over the globe covering the Northern and Southern Hemispheres and the tropics. While capturing the seasonal cycle, the domain area-average seasonal mean initial parameterized energy is weaker than the diagnosed energy by a factor of 3. The best performance in regression analysis is obtained by using a combination of power and exponential functions, which suggests evidence of exponential weakness.
Abstract
Four state-of-the-science numerical weather prediction (NWP) models were used to perform mountain wave (MW)-resolving hindcasts over the Drake Passage of a 10-day period in 2010 with numerous observed MW cases. The Integrated Forecast System (IFS) and the Icosahedral Nonhydrostatic (ICON) model were run at Δx ≈ 9 and 13 km globally. The Weather Research and Forecasting (WRF) Model and the Met Office Unified Model (UM) were both configured with a Δx = 3-km regional domain. All domains had tops near 1 Pa (z ≈ 80 km). These deep domains allowed quantitative validation against Atmospheric Infrared Sounder (AIRS) observations, accounting for observation time, viewing geometry, and radiative transfer. All models reproduced observed middle-atmosphere MWs with remarkable skill. Increased horizontal resolution improved validations. Still, all models underrepresented observed MW amplitudes, even after accounting for model effective resolution and instrument noise, suggesting even at Δx ≈ 3-km resolution, small-scale MWs are underresolved and/or overdiffused. MW drag parameterizations are still necessary in NWP models at current operational resolutions of Δx ≈ 10 km. Upper GW sponge layers in the operationally configured models significantly, artificially reduced MW amplitudes in the upper stratosphere and mesosphere. In the IFS, parameterized GW drags partly compensated this deficiency, but still, total drags were ≈6 times smaller than that resolved at Δx ≈ 3 km. Meridionally propagating MWs significantly enhance zonal drag over the Drake Passage. Interestingly, drag associated with meridional fluxes of zonal momentum (i.e.,
Significance Statement
This study had three purposes: to quantitatively evaluate how well four state-of-the-science weather models could reproduce observed mountain waves (MWs) in the middle atmosphere, to compare the simulated MWs within the models, and to quantitatively evaluate two MW parameterizations in a widely used climate model. These models reproduced observed MWs with remarkable skill. Still, MW parameterizations are necessary in current Δx ≈ 10-km resolution global weather models. Even Δx ≈ 3-km resolution does not appear to be high enough to represent all momentum-fluxing MW scales. Meridionally propagating MWs can significantly influence zonal winds over the Drake Passage. Parameterizations that handle horizontal propagation may need to consider horizontal fluxes of horizontal momentum in order to get the direction of their forcing correct.
Abstract
Four state-of-the-science numerical weather prediction (NWP) models were used to perform mountain wave (MW)-resolving hindcasts over the Drake Passage of a 10-day period in 2010 with numerous observed MW cases. The Integrated Forecast System (IFS) and the Icosahedral Nonhydrostatic (ICON) model were run at Δx ≈ 9 and 13 km globally. The Weather Research and Forecasting (WRF) Model and the Met Office Unified Model (UM) were both configured with a Δx = 3-km regional domain. All domains had tops near 1 Pa (z ≈ 80 km). These deep domains allowed quantitative validation against Atmospheric Infrared Sounder (AIRS) observations, accounting for observation time, viewing geometry, and radiative transfer. All models reproduced observed middle-atmosphere MWs with remarkable skill. Increased horizontal resolution improved validations. Still, all models underrepresented observed MW amplitudes, even after accounting for model effective resolution and instrument noise, suggesting even at Δx ≈ 3-km resolution, small-scale MWs are underresolved and/or overdiffused. MW drag parameterizations are still necessary in NWP models at current operational resolutions of Δx ≈ 10 km. Upper GW sponge layers in the operationally configured models significantly, artificially reduced MW amplitudes in the upper stratosphere and mesosphere. In the IFS, parameterized GW drags partly compensated this deficiency, but still, total drags were ≈6 times smaller than that resolved at Δx ≈ 3 km. Meridionally propagating MWs significantly enhance zonal drag over the Drake Passage. Interestingly, drag associated with meridional fluxes of zonal momentum (i.e.,
Significance Statement
This study had three purposes: to quantitatively evaluate how well four state-of-the-science weather models could reproduce observed mountain waves (MWs) in the middle atmosphere, to compare the simulated MWs within the models, and to quantitatively evaluate two MW parameterizations in a widely used climate model. These models reproduced observed MWs with remarkable skill. Still, MW parameterizations are necessary in current Δx ≈ 10-km resolution global weather models. Even Δx ≈ 3-km resolution does not appear to be high enough to represent all momentum-fluxing MW scales. Meridionally propagating MWs can significantly influence zonal winds over the Drake Passage. Parameterizations that handle horizontal propagation may need to consider horizontal fluxes of horizontal momentum in order to get the direction of their forcing correct.
