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- Author or Editor: Rainer Bleck x
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Abstract
Equations are derived in coordinate-invariant vector notation for the time rate of change of shear and curvature vorticity. These equations are a generalization of equations in natural coordinates derived 30 years ago by Hollmann, and serve to elucidate the conversion process between shear and curvature vorticity. The new form of the conversion term will make it easier to diagnose its magnitude by computer-based objective analysis methods.
Abstract
Equations are derived in coordinate-invariant vector notation for the time rate of change of shear and curvature vorticity. These equations are a generalization of equations in natural coordinates derived 30 years ago by Hollmann, and serve to elucidate the conversion process between shear and curvature vorticity. The new form of the conversion term will make it easier to diagnose its magnitude by computer-based objective analysis methods.
Abstract
Using observed data and model simulations, an attempt is made to verify that baroclinic instability can be viewed as an interaction and mutual amplification of a pair of upper- and lower-tropospheric potential vorticity (PV) perturbations. This view has recently been advanced by Hoskins et al. and McIntyre. Two episodes from March and May 1989, encompassing two lee-cyclogenetic events east of the Rocky Mountains and one over the central Gulf states, are selected to demonstrate this concept. In order to depict the low-level PV maximum which forms infinitely thin sheets of infinite PV, the display of PV in cartesian space is replaced by a display of absolute vorticity in isentropic space. Perspective computer drawings of iso-surfaces of absolute vorticity in three-dimensional space are found to be a convenient means of conveying the desired information.
Abstract
Using observed data and model simulations, an attempt is made to verify that baroclinic instability can be viewed as an interaction and mutual amplification of a pair of upper- and lower-tropospheric potential vorticity (PV) perturbations. This view has recently been advanced by Hoskins et al. and McIntyre. Two episodes from March and May 1989, encompassing two lee-cyclogenetic events east of the Rocky Mountains and one over the central Gulf states, are selected to demonstrate this concept. In order to depict the low-level PV maximum which forms infinitely thin sheets of infinite PV, the display of PV in cartesian space is replaced by a display of absolute vorticity in isentropic space. Perspective computer drawings of iso-surfaces of absolute vorticity in three-dimensional space are found to be a convenient means of conveying the desired information.
Abstract
In a few selected cases of explosive cyclogenesis, a “coarse-mesh” nine-level isentropic prediction model conserving potential geostrophic vorticity is shown to yield dependable 36-hr forecasts of developing cyclones. Stagnant cyclones in adjacent areas are handled with the same degree of accuracy, indicating that numerical instability in the model is not a likely cause of the spontaneous cyclonic development. Tentative conclusions are drawn about the advantages of isentropic, as opposed to isobaric, objective analysis.
Abstract
In a few selected cases of explosive cyclogenesis, a “coarse-mesh” nine-level isentropic prediction model conserving potential geostrophic vorticity is shown to yield dependable 36-hr forecasts of developing cyclones. Stagnant cyclones in adjacent areas are handled with the same degree of accuracy, indicating that numerical instability in the model is not a likely cause of the spontaneous cyclonic development. Tentative conclusions are drawn about the advantages of isentropic, as opposed to isobaric, objective analysis.
Abstract
A numerical model framed in isentropic coordinates is applied to the problem of predicting lee cyclogenesis south of the Alps. Since “Genoa cyclones” during their initial stage are mesoscale phenomena, while mid-tropospheric flow configurations conducive to Genoa cyclogenesis are not, a grid nesting approach is followed in the model to capture both large-scale and mesoscale aspects of the problem. The two grids differ in mesh aim by a factor of 4 and interact in a two-way mode. The model is dry and uses a highly simplified surface drag formulation.
Twenty-four hour predictions carried out on three occasions of observed cyclogenesis show that the model is capable of simulating cyclonic development approximately in the correct location. However, by slightly underpredicting the development of a high-pressure ridge over the eastern Atlantic the model in two of the three cases fails to build up the lee cyclone to the observed strength.
Abstract
A numerical model framed in isentropic coordinates is applied to the problem of predicting lee cyclogenesis south of the Alps. Since “Genoa cyclones” during their initial stage are mesoscale phenomena, while mid-tropospheric flow configurations conducive to Genoa cyclogenesis are not, a grid nesting approach is followed in the model to capture both large-scale and mesoscale aspects of the problem. The two grids differ in mesh aim by a factor of 4 and interact in a two-way mode. The model is dry and uses a highly simplified surface drag formulation.
Twenty-four hour predictions carried out on three occasions of observed cyclogenesis show that the model is capable of simulating cyclonic development approximately in the correct location. However, by slightly underpredicting the development of a high-pressure ridge over the eastern Atlantic the model in two of the three cases fails to build up the lee cyclone to the observed strength.
Abstract
The problem of transforming fields of atmospheric variables from one vertical coordinate system to another without altering their dynamic balance is discussed. A curve fitting scheme applied to the data points in each grid column is proposed which reduces the onset of barotropic imbalances during the transform process.
Abstract
The problem of transforming fields of atmospheric variables from one vertical coordinate system to another without altering their dynamic balance is discussed. A curve fitting scheme applied to the data points in each grid column is proposed which reduces the onset of barotropic imbalances during the transform process.
Abstract
A comparison is made of several ways to combine isentropic with sigma coordinates in a numerical weather prediction model in order to benefit from the advantage of either coordinate. The resulting hybrid model versions appear to be well-behaved numerically. A noise index introduced to provide a measure of external gravitational imbalances shows that hybrid models are somewhat “quieter” than isentropic coordinate models. Results from a related experiment suggest that this reduction in gravitational noise is not simply due to a fundamental noise difference between isentropic and sigma coordinate models but is likely to be a result of the hybridization.
Abstract
A comparison is made of several ways to combine isentropic with sigma coordinates in a numerical weather prediction model in order to benefit from the advantage of either coordinate. The resulting hybrid model versions appear to be well-behaved numerically. A noise index introduced to provide a measure of external gravitational imbalances shows that hybrid models are somewhat “quieter” than isentropic coordinate models. Results from a related experiment suggest that this reduction in gravitational noise is not simply due to a fundamental noise difference between isentropic and sigma coordinate models but is likely to be a result of the hybridization.
Abstract
Two limited-area prediction models in isentropic coordinates, one based on potential vorticity conservation and one using the primitive equations of motion, are tested on 50 synoptic cases chosen from winter and spring of 1972/73. Both models disregard diabatic processes, but incorporate variable terrain height. Numerical instabilities caused by overturning or entwining coordinate surfaces appear to be no problem in this approach, and the gravitational noise generated at the lower boundary in the primitive equation model is shown to remain well within acceptable limits. Skill scores based on displacement errors of surface cyclones and on correlations between predicted and observed sea-level pressure gradients indicate that neither model at this stage can compete with the six-level hemispheric model used by the National Weather Service. Of the two isentropic models, the one using primitive equations shows better skill than the potential vorticity model.
Abstract
Two limited-area prediction models in isentropic coordinates, one based on potential vorticity conservation and one using the primitive equations of motion, are tested on 50 synoptic cases chosen from winter and spring of 1972/73. Both models disregard diabatic processes, but incorporate variable terrain height. Numerical instabilities caused by overturning or entwining coordinate surfaces appear to be no problem in this approach, and the gravitational noise generated at the lower boundary in the primitive equation model is shown to remain well within acceptable limits. Skill scores based on displacement errors of surface cyclones and on correlations between predicted and observed sea-level pressure gradients indicate that neither model at this stage can compete with the six-level hemispheric model used by the National Weather Service. Of the two isentropic models, the one using primitive equations shows better skill than the potential vorticity model.
Abstract
A method for analyzing height fields from simultaneous observations of height and wind is proposed which combines Gandin's optimum interpolation concept with the classical approach of extrapolating height values geostrophically to a grid point from surrounding stations. While recently developed multivariate optimum interpolation techniques using both height and wind data result in a somewhat smaller rms error of the analyzed height field than the present method, they require approximately 33 times as much computer time.
Abstract
A method for analyzing height fields from simultaneous observations of height and wind is proposed which combines Gandin's optimum interpolation concept with the classical approach of extrapolating height values geostrophically to a grid point from surrounding stations. While recently developed multivariate optimum interpolation techniques using both height and wind data result in a somewhat smaller rms error of the analyzed height field than the present method, they require approximately 33 times as much computer time.
Abstract
A numerical experiment is described which explores the relationship between upper-level potential vorticity advection and cyclogenesis on the leeward side of mountain barriers. A multilevel primitive equation model framed in isentropic coordinates is used to simulate the growth of a wave disturbance on the cold front associated with a preexisting “parent” cyclone. The effect of a mountain barrier placed in the path of the advancing cold front and the effect of an enhanced upper-level jet streak on the growth rate of the disturbance are investigated. Enhancement of the jet streak is accomplished by altering the geostrophic potential vorticity in a region upstream of the mountain barrier and solving for the corresponding man and geostrophic velocity field. The experiment suggests a strong connection between the intensity of the jet weak impinging on the barrier and the pressure fall in the lee. We also find that the strongest leeside pressure fall in this experiment is not accompanied by a conversion of available potential energy to kinetic energy. This suggests that geostrophic adjustment processes, rather than baroclinic instability, may cause the rapid initial growth of some, though possibly not all, lee cyclones.
Abstract
A numerical experiment is described which explores the relationship between upper-level potential vorticity advection and cyclogenesis on the leeward side of mountain barriers. A multilevel primitive equation model framed in isentropic coordinates is used to simulate the growth of a wave disturbance on the cold front associated with a preexisting “parent” cyclone. The effect of a mountain barrier placed in the path of the advancing cold front and the effect of an enhanced upper-level jet streak on the growth rate of the disturbance are investigated. Enhancement of the jet streak is accomplished by altering the geostrophic potential vorticity in a region upstream of the mountain barrier and solving for the corresponding man and geostrophic velocity field. The experiment suggests a strong connection between the intensity of the jet weak impinging on the barrier and the pressure fall in the lee. We also find that the strongest leeside pressure fall in this experiment is not accompanied by a conversion of available potential energy to kinetic energy. This suggests that geostrophic adjustment processes, rather than baroclinic instability, may cause the rapid initial growth of some, though possibly not all, lee cyclones.
Abstract
A two-layer isentropic model is used to examine the parameters controlling the severity of cold-air outbreaks east of the Rocky Mountains, and in particular the channeling effect of the mountain range. The case that is scrutinized is the cold-air outbreak of early February 1989. The parameters investigated include (a) the baro-clinicity, expressed as the ratio of upper- to lower-layer zonal scale velocities, (b) the Rossby number; (c) the height of the topography;(d)the initial longitudinal position of the cold air mass relative to the mountain ridge; and (e) the presence of a wave in the upper-level flow. It is found that the Rossby number determines the intensity of a cold-air outbreak, whereas the baroclinicity as well as the height of the orography and the initial position of the cold air mass control the extent to which the outbreak is channeled by the mountain range. An upper-level trough over the central United States favors the evolution of an outbreak.
Abstract
A two-layer isentropic model is used to examine the parameters controlling the severity of cold-air outbreaks east of the Rocky Mountains, and in particular the channeling effect of the mountain range. The case that is scrutinized is the cold-air outbreak of early February 1989. The parameters investigated include (a) the baro-clinicity, expressed as the ratio of upper- to lower-layer zonal scale velocities, (b) the Rossby number; (c) the height of the topography;(d)the initial longitudinal position of the cold air mass relative to the mountain ridge; and (e) the presence of a wave in the upper-level flow. It is found that the Rossby number determines the intensity of a cold-air outbreak, whereas the baroclinicity as well as the height of the orography and the initial position of the cold air mass control the extent to which the outbreak is channeled by the mountain range. An upper-level trough over the central United States favors the evolution of an outbreak.
