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- Author or Editor: Stephen D. Eckermann x
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Abstract
A Fourier method is used to model mountain waves that have nearby turning points in a wind jet. In Fourier space, the propagation equations are solved by ray theory. To correct for the ray singularity at a turning point without time-consuming special-function evaluations, the ray solution is linearly interpolated across the breakdown region. The Fourier solutions for the spatial wavefield are compared with mesoscale model simulations in two cases: two-dimensional flow over idealized topography with uniform stratification and a sech-squared wind profile and three-dimensional flow over the island of Jan Mayen with stratification and wind profiles taken from radiosonde measurements. The latter case reveals the partial transmission of trapped mountain waves into the stratosphere.
Abstract
A Fourier method is used to model mountain waves that have nearby turning points in a wind jet. In Fourier space, the propagation equations are solved by ray theory. To correct for the ray singularity at a turning point without time-consuming special-function evaluations, the ray solution is linearly interpolated across the breakdown region. The Fourier solutions for the spatial wavefield are compared with mesoscale model simulations in two cases: two-dimensional flow over idealized topography with uniform stratification and a sech-squared wind profile and three-dimensional flow over the island of Jan Mayen with stratification and wind profiles taken from radiosonde measurements. The latter case reveals the partial transmission of trapped mountain waves into the stratosphere.
Abstract
During austral winter, and away from orographic maxima or “hot spots,” stratospheric gravity waves in both satellite observations and Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) data reveal enhanced amplitudes in a broad midlatitude belt extending across the Southern Ocean from east of the Andes to south of New Zealand. The peak latitude of this feature slowly migrates poleward from 50° to 60°S. Wave amplitudes are much weaker across the midlatitude Pacific Ocean. These features of the wave field are in striking agreement with diagnostics of baroclinic growth rates in the troposphere associated with midlatitude winter storm tracks and the climatology of the midlatitude jet. This correlation suggests that these features of the stratospheric gravity wave field are controlled by geographical variations of tropospheric nonorographic gravity wave sources in winter storm tracks: spontaneous adjustment emission from the midlatitude winter jet, frontogenesis, and convection.
Abstract
During austral winter, and away from orographic maxima or “hot spots,” stratospheric gravity waves in both satellite observations and Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) data reveal enhanced amplitudes in a broad midlatitude belt extending across the Southern Ocean from east of the Andes to south of New Zealand. The peak latitude of this feature slowly migrates poleward from 50° to 60°S. Wave amplitudes are much weaker across the midlatitude Pacific Ocean. These features of the wave field are in striking agreement with diagnostics of baroclinic growth rates in the troposphere associated with midlatitude winter storm tracks and the climatology of the midlatitude jet. This correlation suggests that these features of the stratospheric gravity wave field are controlled by geographical variations of tropospheric nonorographic gravity wave sources in winter storm tracks: spontaneous adjustment emission from the midlatitude winter jet, frontogenesis, and convection.
Abstract
Large-amplitude stratospheric gravity waves over the southern Andes and Drake Passage, as observed by the Atmospheric Infrared Sounder (AIRS) on 8–9 August 2010, are modeled and studied using a deep (0–70 km) version of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model. The simulated tropospheric waves are generated by flow over the high central Andes ridge and the Patagonian peaks in the southern Andes. Some waves emanating from Patagonia propagate southeastward across Drake Passage into the stratosphere over a horizontal distance of more than 1000 km. The wave momentum flux is characterized by a tropospheric maximum over Patagonia that splits into two comparable maxima in the stratosphere: one located directly over the terrain and the other tilting southward with altitude.
Using spatial ray-tracing techniques and flow conditions derived from the numerical simulation, the authors find that waves that originate from the high ridge in the Central Andes are absorbed by a critical level in the lower stratosphere. The three-dimensional waves originating from Patagonia could be separated into three families—namely, a northeast-propagating family, which is absorbed by a critical level between 15 and 20 km; a localized family, which breaks down in the stratosphere and lower mesosphere directly above Patagonia; and a southeast-propagating family, which forms the observed linear stratospheric wave patterns oriented across Drake Passage. The southward group propagation, assisted by lateral wave refraction due to persistent meridional shear of the zonal winds, leads to stratospheric wave breaking and drag near 60°S, well south of the parent orography.
Abstract
Large-amplitude stratospheric gravity waves over the southern Andes and Drake Passage, as observed by the Atmospheric Infrared Sounder (AIRS) on 8–9 August 2010, are modeled and studied using a deep (0–70 km) version of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) model. The simulated tropospheric waves are generated by flow over the high central Andes ridge and the Patagonian peaks in the southern Andes. Some waves emanating from Patagonia propagate southeastward across Drake Passage into the stratosphere over a horizontal distance of more than 1000 km. The wave momentum flux is characterized by a tropospheric maximum over Patagonia that splits into two comparable maxima in the stratosphere: one located directly over the terrain and the other tilting southward with altitude.
Using spatial ray-tracing techniques and flow conditions derived from the numerical simulation, the authors find that waves that originate from the high ridge in the Central Andes are absorbed by a critical level in the lower stratosphere. The three-dimensional waves originating from Patagonia could be separated into three families—namely, a northeast-propagating family, which is absorbed by a critical level between 15 and 20 km; a localized family, which breaks down in the stratosphere and lower mesosphere directly above Patagonia; and a southeast-propagating family, which forms the observed linear stratospheric wave patterns oriented across Drake Passage. The southward group propagation, assisted by lateral wave refraction due to persistent meridional shear of the zonal winds, leads to stratospheric wave breaking and drag near 60°S, well south of the parent orography.
Abstract
Gravity waves are frequently observed in the stratosphere, trailing long distances from mid- to high-latitude topography. Two such trailing-wave events documented over New Zealand are examined using observations, numerical simulations, and ray-tracing analysis to explore and document stratospheric trailing-wave characteristics and formation mechanisms. We find that the trailing waves over New Zealand are orographically generated and regulated by several processes, including interaction between terrain and mountaintop winds, critical-level absorption, and lateral wave refraction. Among these, the interaction between topography and low-level winds determines the perturbation energy distribution over horizontal scales and directions near the wave source, and accordingly, trailing waves are sensitive to terrain features and low-level winds. Terrain-forced wave modes are filtered by absorption associated with directional wind shear and Jones critical levels. The former plays a role in defining wave-beam orientation, and the latter sets an upper limit for the permissible horizontal wavelength of trailing waves. On propagating into the stratosphere, these orographic gravity waves are subject to horizontal refraction associated with the meridional shear in the stratospheric westerlies, which tends to elongate the wave beams pointing toward stronger westerlies and shorten the wave beams on the opposite side.
Abstract
Gravity waves are frequently observed in the stratosphere, trailing long distances from mid- to high-latitude topography. Two such trailing-wave events documented over New Zealand are examined using observations, numerical simulations, and ray-tracing analysis to explore and document stratospheric trailing-wave characteristics and formation mechanisms. We find that the trailing waves over New Zealand are orographically generated and regulated by several processes, including interaction between terrain and mountaintop winds, critical-level absorption, and lateral wave refraction. Among these, the interaction between topography and low-level winds determines the perturbation energy distribution over horizontal scales and directions near the wave source, and accordingly, trailing waves are sensitive to terrain features and low-level winds. Terrain-forced wave modes are filtered by absorption associated with directional wind shear and Jones critical levels. The former plays a role in defining wave-beam orientation, and the latter sets an upper limit for the permissible horizontal wavelength of trailing waves. On propagating into the stratosphere, these orographic gravity waves are subject to horizontal refraction associated with the meridional shear in the stratospheric westerlies, which tends to elongate the wave beams pointing toward stronger westerlies and shorten the wave beams on the opposite side.
Abstract
Power spectral densities (PSDs) of mesoscale fluctuations of temperature and rate of change of temperature (heating–cooling rate) due to a spectrum of stratospheric gravity waves are derived using canonical spectral forms based on observations and linear gravity wave theory. The parameterization developed here assumes a continuous distribution of horizontal wave phase speeds, as opposed to a previous spectral parameterization in which all waves were assigned stationary ground-based phase speeds. Significantly different heating–cooling rate PSDs result in each case. The differences are largest at small horizontal scales, where the continuous phase-speed parameterization yields heating–cooling rate PSDs that are several orders of magnitude smaller than in the stationary phase-speed parameterization. A simple Monte Carlo method is used to synthesize randomly phased temperature perturbation time series within tagged air parcels using either spectral parameterization. These time series are incorporated into a nonequilibrium, microphysical trajectory-box model to assess the microphysical consequences of each parameterization. Collated results yield a “natural” geophysical scatter of instantaneous aerosol volumes within air parcels away from equilibrium conditions. The amount of scatter was much smaller when the continuous phase-speed parameterization was used.
Abstract
Power spectral densities (PSDs) of mesoscale fluctuations of temperature and rate of change of temperature (heating–cooling rate) due to a spectrum of stratospheric gravity waves are derived using canonical spectral forms based on observations and linear gravity wave theory. The parameterization developed here assumes a continuous distribution of horizontal wave phase speeds, as opposed to a previous spectral parameterization in which all waves were assigned stationary ground-based phase speeds. Significantly different heating–cooling rate PSDs result in each case. The differences are largest at small horizontal scales, where the continuous phase-speed parameterization yields heating–cooling rate PSDs that are several orders of magnitude smaller than in the stationary phase-speed parameterization. A simple Monte Carlo method is used to synthesize randomly phased temperature perturbation time series within tagged air parcels using either spectral parameterization. These time series are incorporated into a nonequilibrium, microphysical trajectory-box model to assess the microphysical consequences of each parameterization. Collated results yield a “natural” geophysical scatter of instantaneous aerosol volumes within air parcels away from equilibrium conditions. The amount of scatter was much smaller when the continuous phase-speed parameterization was used.
Abstract
A Fourier method is combined with a mesoscale model to simulate mountain waves. The mesoscale model describes the nonlinear low-level flow and predicts the emerging wave field above the mountain. This solution serves as the lower boundary condition for the Fourier method, which follows the waves upward to much higher altitudes and downward to the ground to examine parameterizations for the orography and the lower boundary condition. A high-drag case with a Froude number of ⅔ is presented.
Abstract
A Fourier method is combined with a mesoscale model to simulate mountain waves. The mesoscale model describes the nonlinear low-level flow and predicts the emerging wave field above the mountain. This solution serves as the lower boundary condition for the Fourier method, which follows the waves upward to much higher altitudes and downward to the ground to examine parameterizations for the orography and the lower boundary condition. A high-drag case with a Froude number of ⅔ is presented.
Abstract
Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.
Abstract
Gravity wave (GW) momentum and energy deposition are large components of the momentum and heat budgets of the stratosphere and mesosphere, affecting predictability across scales. Since weather and climate models cannot resolve the entire GW spectrum, GW parameterizations are required. Tuning these parameterizations is time-consuming and must be repeated whenever model configurations are changed. We introduce a self-tuning approach, called GW parameter retrieval (GWPR), applied when the model is coupled to a data assimilation (DA) system. A key component of GWPR is a linearized model of the sensitivity of model wind and temperature to the GW parameters, which is calculated using an ensemble of nonlinear forecasts with perturbed parameters. GWPR calculates optimal parameters using an adaptive grid search that reduces DA analysis increments via a cost-function minimization. We test GWPR within the Navy Global Environmental Model (NAVGEM) using three latitude-dependent GW parameters: peak momentum flux, phase-speed width of the Gaussian source spectrum, and phase-speed weighting relative to the source-level wind. Compared to a baseline experiment with fixed parameters, GWPR reduces analysis increments and improves 5-day mesospheric forecasts. Relative to the baseline, retrieved parameters reveal enhanced source-level fluxes and westward shift of the wave spectrum in the winter extratropics, which we relate to seasonal variations in frontogenesis. The GWPR reduces stratospheric increments near 60°S during austral winter, compensating for excessive baseline nonorographic GW drag. Tropical sensitivity is weaker due to significant absorption of GW in the stratosphere, resulting in less confidence in tropical GWPR values.
Abstract
A methodology is presented for objectively optimizing nonorographic gravity wave source parameters to minimize forecast error for target regions and forecast lead times. In this study, we employ a high-altitude version of the Navy Global Environmental Model (NAVGEM-HA) to ascertain the forcing needed to minimize hindcast errors in the equatorial lower stratospheric zonal-mean zonal winds in order to improve forecasts of the quasi-biennial oscillation (QBO) over seasonal time scales. Because subgrid-scale wave effects play a large role in driving the QBO, this method leverages the nonorographic gravity wave drag (GWD) parameterization scheme to provide the necessary forcing. To better constrain the GWD source parameters, we utilize ensembles of NAVGEM-HA hindcasts over the 2014–16 period with perturbed source parameters and develop a cost function to minimize errors in the equatorial lower stratosphere compared to analysis. Thus, we may determine the set of GWD source parameters that yields a forecast state that most closely agrees with observed QBO winds over each optimization time interval. Results show that the source momentum flux and phase speed spectrum width are the most important parameters. The seasonal evolution of optimal parameter value, specifically a robust semiannual periodicity in the source strength, is also revealed. Changes in optimal source parameters with increasing forecast lead time are seen, as the GWD parameterization takes on a more active role as QBO driver at longer forecast lengths. Implementation of a semiannually varying source function at the equator provides RMS error improvement in QBO winds over the default constant value.
Abstract
A methodology is presented for objectively optimizing nonorographic gravity wave source parameters to minimize forecast error for target regions and forecast lead times. In this study, we employ a high-altitude version of the Navy Global Environmental Model (NAVGEM-HA) to ascertain the forcing needed to minimize hindcast errors in the equatorial lower stratospheric zonal-mean zonal winds in order to improve forecasts of the quasi-biennial oscillation (QBO) over seasonal time scales. Because subgrid-scale wave effects play a large role in driving the QBO, this method leverages the nonorographic gravity wave drag (GWD) parameterization scheme to provide the necessary forcing. To better constrain the GWD source parameters, we utilize ensembles of NAVGEM-HA hindcasts over the 2014–16 period with perturbed source parameters and develop a cost function to minimize errors in the equatorial lower stratosphere compared to analysis. Thus, we may determine the set of GWD source parameters that yields a forecast state that most closely agrees with observed QBO winds over each optimization time interval. Results show that the source momentum flux and phase speed spectrum width are the most important parameters. The seasonal evolution of optimal parameter value, specifically a robust semiannual periodicity in the source strength, is also revealed. Changes in optimal source parameters with increasing forecast lead time are seen, as the GWD parameterization takes on a more active role as QBO driver at longer forecast lengths. Implementation of a semiannually varying source function at the equator provides RMS error improvement in QBO winds over the default constant value.
Abstract
Past investigations have documented large divergent wind anomalies in stratospheric reanalyses over steep terrain, which were attributed to discretization errors produced by the terrain-following (sigma) vertical coordinate in the forecast model. However, forecasting experiments have reported negligible differences in skill between sigma- and hybrid-coordinate models. This leads to the paradoxical conclusion that discretization errors in the forecast model yield significant stratospheric analysis errors, but insignificant stratospheric forecast errors. The authors reexamine this issue by performing two forecast-assimilation experiments that are identical except for the vertical coordinate: one uses a sigma coordinate and the other uses a hybrid coordinate. The sigma-coordinate analyses exhibit large divergent wind anomalies over terrain that extend from the surface to the model top and distort explicitly resolved orographic gravity waves. Above the tropopause, divergent wind errors are suppressed by an order of magnitude or more in the hybrid-coordinate analyses. Over a 3-month period, stratospheric skill scores in the hybrid experiment show statistically significant improvements relative to the sigma experiment. Previous studies, which found no such differences, all used forecasts initialized from a common archived analysis. The results show that the dominant pathway for error growth and net skill impacts is via 0–9-h forecast backgrounds cycling successively through the data assimilation phase without significant observational correction. The skill impacts noted here should further motivate weather and climate models to adopt a hybrid coordinate with the best error suppression characteristics for a given modeling application.
Abstract
Past investigations have documented large divergent wind anomalies in stratospheric reanalyses over steep terrain, which were attributed to discretization errors produced by the terrain-following (sigma) vertical coordinate in the forecast model. However, forecasting experiments have reported negligible differences in skill between sigma- and hybrid-coordinate models. This leads to the paradoxical conclusion that discretization errors in the forecast model yield significant stratospheric analysis errors, but insignificant stratospheric forecast errors. The authors reexamine this issue by performing two forecast-assimilation experiments that are identical except for the vertical coordinate: one uses a sigma coordinate and the other uses a hybrid coordinate. The sigma-coordinate analyses exhibit large divergent wind anomalies over terrain that extend from the surface to the model top and distort explicitly resolved orographic gravity waves. Above the tropopause, divergent wind errors are suppressed by an order of magnitude or more in the hybrid-coordinate analyses. Over a 3-month period, stratospheric skill scores in the hybrid experiment show statistically significant improvements relative to the sigma experiment. Previous studies, which found no such differences, all used forecasts initialized from a common archived analysis. The results show that the dominant pathway for error growth and net skill impacts is via 0–9-h forecast backgrounds cycling successively through the data assimilation phase without significant observational correction. The skill impacts noted here should further motivate weather and climate models to adopt a hybrid coordinate with the best error suppression characteristics for a given modeling application.
Abstract
Gravity wave perturbations in 15-μm nadir radiances from the Atmospheric Infrared Sounder (AIRS) and Cross-Track Infrared Sounder (CrIS) informed scientific flight planning for the Deep Propagating Gravity Wave Experiment (DEEPWAVE). AIRS observations from 2003 to 2011 identified the South Island of New Zealand during June–July as a “natural laboratory” for observing deep-propagating gravity wave dynamics. Near-real-time AIRS and CrIS gravity wave products monitored wave activity in and around New Zealand continuously within 10 regions of scientific interest, providing nowcast guidance and validation for flight planners. A novel technique used these gravity wave products to validate upstream forecasts of nonorographic gravity waves with 1–2-day lead times, providing time to plan flight intercepts as tropospheric westerlies brought forecast source regions into range. Postanalysis verifies the choice of 15 μm radiances for nowcasting, since 4.3-μm gravity wave products yielded spurious diurnal cycles, provided no altitude sensitivity, and proved relatively insensitive to deep gravity wave activity over the South Island. Comparisons of DEEPWAVE flight tracks with AIRS and CrIS gravity wave maps highlight successful repeated vectoring of the aircraft into regions of deep orographic and nonorographic gravity wave activity, and how background winds control the amplitude of waves in radiance perturbation maps. We discuss how gravity wave information in AIRS and CrIS radiances might be directly assimilated into future operational forecasting systems.
Abstract
Gravity wave perturbations in 15-μm nadir radiances from the Atmospheric Infrared Sounder (AIRS) and Cross-Track Infrared Sounder (CrIS) informed scientific flight planning for the Deep Propagating Gravity Wave Experiment (DEEPWAVE). AIRS observations from 2003 to 2011 identified the South Island of New Zealand during June–July as a “natural laboratory” for observing deep-propagating gravity wave dynamics. Near-real-time AIRS and CrIS gravity wave products monitored wave activity in and around New Zealand continuously within 10 regions of scientific interest, providing nowcast guidance and validation for flight planners. A novel technique used these gravity wave products to validate upstream forecasts of nonorographic gravity waves with 1–2-day lead times, providing time to plan flight intercepts as tropospheric westerlies brought forecast source regions into range. Postanalysis verifies the choice of 15 μm radiances for nowcasting, since 4.3-μm gravity wave products yielded spurious diurnal cycles, provided no altitude sensitivity, and proved relatively insensitive to deep gravity wave activity over the South Island. Comparisons of DEEPWAVE flight tracks with AIRS and CrIS gravity wave maps highlight successful repeated vectoring of the aircraft into regions of deep orographic and nonorographic gravity wave activity, and how background winds control the amplitude of waves in radiance perturbation maps. We discuss how gravity wave information in AIRS and CrIS radiances might be directly assimilated into future operational forecasting systems.
