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- Author or Editor: WALTER JAMES KOSS x
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Abstract
The physical stability of perturbation motions in a conditionally unstable tropical atmosphere at rest is examined under CISK forcing. The governing linear multi-layer primitive equations are formulated into an eigenvalue problem for the unconditional heating case. This analysis yields propagation speeds, growth rates and vertical structure for the modes supported by the model. The specified parameters are the vertical distribution of diabatic heating, the base state temperature structure, boundary layer specific humidity, lateral mixing coefficients for momentum and temperature, surface friction coefficient, Coriolis parameter and perturbation wavelength. A variety of unstable quasi-balanced modes are found, some of which have small e-folding times (on the order of days) with a cyclone-scale preferred wavelength; for these modes a pronounced short-wave cutoff is essentially independent of lateral mixing. For a well-delineated vertical heating profile, and certain values of the physical parameters, the vertical structure of these modes resembles that of the formative stage of a tropical cyclone. Internal gravity modes are found which are unstable; the external gravity mode damps in all cases. These results hold for both a three-layer and a seven-layer model. With coarse vertical resolution, the results are strongly dependent on the vertical staggering of the dependent variables; increasing the vertical resolution of the model eliminates differences due to the choice of staggering, and introduces a variety of unstable larger (cyclone) scale disturbances in response to variations in the vertical heating distribution.
Abstract
The physical stability of perturbation motions in a conditionally unstable tropical atmosphere at rest is examined under CISK forcing. The governing linear multi-layer primitive equations are formulated into an eigenvalue problem for the unconditional heating case. This analysis yields propagation speeds, growth rates and vertical structure for the modes supported by the model. The specified parameters are the vertical distribution of diabatic heating, the base state temperature structure, boundary layer specific humidity, lateral mixing coefficients for momentum and temperature, surface friction coefficient, Coriolis parameter and perturbation wavelength. A variety of unstable quasi-balanced modes are found, some of which have small e-folding times (on the order of days) with a cyclone-scale preferred wavelength; for these modes a pronounced short-wave cutoff is essentially independent of lateral mixing. For a well-delineated vertical heating profile, and certain values of the physical parameters, the vertical structure of these modes resembles that of the formative stage of a tropical cyclone. Internal gravity modes are found which are unstable; the external gravity mode damps in all cases. These results hold for both a three-layer and a seven-layer model. With coarse vertical resolution, the results are strongly dependent on the vertical staggering of the dependent variables; increasing the vertical resolution of the model eliminates differences due to the choice of staggering, and introduces a variety of unstable larger (cyclone) scale disturbances in response to variations in the vertical heating distribution.
Abstract
A linearized, two-level forecast model with known analytic solution is numerically integrated to examine the behavior of the accumulated error (truncation and machine word “round-off” error). The results indicate that for linear models numerically integrated with centered differences: 1) the ratio of space increment to disturbance wavelength that yields sufficient accuracy in a reasonable amount of computation real time is on the order of 10−1 to 10−2; 2) the largest time increment consistent with the stability criterion should be used for computation expediency.
Computations performed on computers having different word lengths did not yield significant differences in the results for this model integrated out to 7 days.
Abstract
A linearized, two-level forecast model with known analytic solution is numerically integrated to examine the behavior of the accumulated error (truncation and machine word “round-off” error). The results indicate that for linear models numerically integrated with centered differences: 1) the ratio of space increment to disturbance wavelength that yields sufficient accuracy in a reasonable amount of computation real time is on the order of 10−1 to 10−2; 2) the largest time increment consistent with the stability criterion should be used for computation expediency.
Computations performed on computers having different word lengths did not yield significant differences in the results for this model integrated out to 7 days.
Abstract
Numerical experiments were performed with variable resolution two-dimensional rectangular Cartesian grids. The shallow-water equations were integrated on several variable-mesh grids and on a constant increment fine-resolution grid; the method of integration used the “box” technique for spatial representation. The grids were designed to be used in numerical experiments that examine vortex-type motions that may be embedded in a fairly uniform basic current. With this in mind, two systems were investigated: (1) a closed system containing a balanced vortex and (2) a semiopen system with east-west cyclic continuity containing a moderately strong easterly jet. The results indicate that, for a weak vortex embedded in a zonal current, a 2-step “telescope”-type grid can be used in numerical integrations with success; that is, the incurred error is relatively small and the computation time and computer memory requirements are not excessive. For an intense vortex, a graded-type grid yields a relatively better numerical integration at the expense of an increase in computation time.
Abstract
Numerical experiments were performed with variable resolution two-dimensional rectangular Cartesian grids. The shallow-water equations were integrated on several variable-mesh grids and on a constant increment fine-resolution grid; the method of integration used the “box” technique for spatial representation. The grids were designed to be used in numerical experiments that examine vortex-type motions that may be embedded in a fairly uniform basic current. With this in mind, two systems were investigated: (1) a closed system containing a balanced vortex and (2) a semiopen system with east-west cyclic continuity containing a moderately strong easterly jet. The results indicate that, for a weak vortex embedded in a zonal current, a 2-step “telescope”-type grid can be used in numerical integrations with success; that is, the incurred error is relatively small and the computation time and computer memory requirements are not excessive. For an intense vortex, a graded-type grid yields a relatively better numerical integration at the expense of an increase in computation time.
Abstract
The known general solution of the system of linearized equations for non-viscous, adiabatic, quasi-hydrostatic flow on an equatorially oriented β-plane is examined in detail for various boundary conditions imposed on the motion. The base state is a space-time invariant zonal current. The particular solutions examined are those in which the meridional wind component is distributed either symmetrically or asymmetrically about the equator, and is constrained either to vanish at finite distance from the equator or to decay exponentially at large distance from the equator. The various solutions considered depict disturbances which are characterized by (1) very small values of divergence which increase with wavelength (in most cases), (2) relative vorticity which is meteorologically reasonable, and (3) in general, a non-geostrophic wind-pressure relationship.
Abstract
The known general solution of the system of linearized equations for non-viscous, adiabatic, quasi-hydrostatic flow on an equatorially oriented β-plane is examined in detail for various boundary conditions imposed on the motion. The base state is a space-time invariant zonal current. The particular solutions examined are those in which the meridional wind component is distributed either symmetrically or asymmetrically about the equator, and is constrained either to vanish at finite distance from the equator or to decay exponentially at large distance from the equator. The various solutions considered depict disturbances which are characterized by (1) very small values of divergence which increase with wavelength (in most cases), (2) relative vorticity which is meteorologically reasonable, and (3) in general, a non-geostrophic wind-pressure relationship.
Abstract
A method for objectively analyzing the geopotential height field on a constant pressure surface using reported upper-air data is described. Special attention is given to the analysis in data sparse regions, in particular, the Tropics. Wind-height relationships are used to augment the reported data by extrapolation of the reported height values into the data voids. The augmented data are used in a least-squares process to generate a polynomial surface which is used as the initial guess in an iterative-correction routine. The resultant objective analysis is comparable to the subjective analysis produced by an experienced analyst. Comparative examples are presented in which the region of analysis encompasses the Caribbean Sea, Gulf of Mexico, and adjacent areas.
Abstract
A method for objectively analyzing the geopotential height field on a constant pressure surface using reported upper-air data is described. Special attention is given to the analysis in data sparse regions, in particular, the Tropics. Wind-height relationships are used to augment the reported data by extrapolation of the reported height values into the data voids. The augmented data are used in a least-squares process to generate a polynomial surface which is used as the initial guess in an iterative-correction routine. The resultant objective analysis is comparable to the subjective analysis produced by an experienced analyst. Comparative examples are presented in which the region of analysis encompasses the Caribbean Sea, Gulf of Mexico, and adjacent areas.
Abstract
In this Paper we present the geometry and intensity of the mean east–west circulation during the northern winter. We show that near the equatorial latitudes two pronounced regions of divergent mass outflow in the upper troposphere are found near the convective regions over the northwestern part of South America and Indonesia. The intensity of the east–west circulation is shown to be of the order of 1 m sec−1 which is comparable to the intensity of the Hadley circulation. The divergent streamlines are shown to be important for the maintenance of the three waves of the subtropical westerly jet in the Northern Hemisphere, and are shown to exhibit asymptotes of convergence in the regions of mid-oceanic upper tropospheric troughs over the tropical southern oceans. Kinetic energy exchanges for a tropical belt 15S to 15N at 200 mb are expressed as a function of zonal wavenumber. Results for northern summer and winter seasons are compared. We find that wave interactions with the mean zonal flow differ in the two seasons. During the northern summer the long waves (wavenumbers 1 and 2) transfer kinetic energy to the zonal flow which in turn transfers kinetic energy to the short waves (wavenumbers 6, 7 and 8). During the northern winter the opposite occurs: long waves receive kinetic energy from the zonal flow while short waves transfer kinetic energy to the zonal flow.
Finally, we evaluate the generation of eddy kinetic energy by the mean east–west circulations during the two seasons. We show that the east–west circulations are thermally direct, i.e., there is a generation of eddy kinetic energy, on horizontal scales >10,000 km. We furthermore find that this generation during the northern summer is about an order of magnitude larger than for the northern winter.
Abstract
In this Paper we present the geometry and intensity of the mean east–west circulation during the northern winter. We show that near the equatorial latitudes two pronounced regions of divergent mass outflow in the upper troposphere are found near the convective regions over the northwestern part of South America and Indonesia. The intensity of the east–west circulation is shown to be of the order of 1 m sec−1 which is comparable to the intensity of the Hadley circulation. The divergent streamlines are shown to be important for the maintenance of the three waves of the subtropical westerly jet in the Northern Hemisphere, and are shown to exhibit asymptotes of convergence in the regions of mid-oceanic upper tropospheric troughs over the tropical southern oceans. Kinetic energy exchanges for a tropical belt 15S to 15N at 200 mb are expressed as a function of zonal wavenumber. Results for northern summer and winter seasons are compared. We find that wave interactions with the mean zonal flow differ in the two seasons. During the northern summer the long waves (wavenumbers 1 and 2) transfer kinetic energy to the zonal flow which in turn transfers kinetic energy to the short waves (wavenumbers 6, 7 and 8). During the northern winter the opposite occurs: long waves receive kinetic energy from the zonal flow while short waves transfer kinetic energy to the zonal flow.
Finally, we evaluate the generation of eddy kinetic energy by the mean east–west circulations during the two seasons. We show that the east–west circulations are thermally direct, i.e., there is a generation of eddy kinetic energy, on horizontal scales >10,000 km. We furthermore find that this generation during the northern summer is about an order of magnitude larger than for the northern winter.
