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- Author or Editor: YOSHIKAZU SASAKI x
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Abstract
The formation of a prefrontal squall line is studied, based on a numerical method of solving the modified equation of motion, continuity (mass and moisture content), and thermodynamics simultaneously. Due to the limited capacity of the electronic computer used (IBM 650), computations in this experiment are necessarily simplified, and this preliminary study is made for two idealized cases both of which consider conditions in advance of an intense cold front. The first case treats moist air at low levels with dry air aloft; the second considers a strong southerly jet-like flow at low levels. From results obtained, it is shown that a significant factor for squall-line formation is the unbalance between thermal wind and actual wind shear. Also, the role of a strong southerly flow at low levels is indirect and appears to be that of supplying moisture from ocean areas.
Abstract
The formation of a prefrontal squall line is studied, based on a numerical method of solving the modified equation of motion, continuity (mass and moisture content), and thermodynamics simultaneously. Due to the limited capacity of the electronic computer used (IBM 650), computations in this experiment are necessarily simplified, and this preliminary study is made for two idealized cases both of which consider conditions in advance of an intense cold front. The first case treats moist air at low levels with dry air aloft; the second considers a strong southerly jet-like flow at low levels. From results obtained, it is shown that a significant factor for squall-line formation is the unbalance between thermal wind and actual wind shear. Also, the role of a strong southerly flow at low levels is indirect and appears to be that of supplying moisture from ocean areas.
Abstract
The weighting factors used in conventional objective analysis methods are reviewed on the basis of numerical variational analysis. Special emphasis is placed on anisotropy (ellipticity) of the factors. The weighting factors of the objective analysis methods were empirically determined and are two dimensional in a horizontal plane (x, y). Most of these weighting factors are isotropic. However, anisotropic weighting factors have recently been used to give greater weight to the upstream and downstream observations as compared to those of the crosswind direction.
A simple advection equation is used as a dynamical constraint in the numerical variational analysis in order to take into account quantitatively the effect of wind direction and speed on the anisotropy. A simple low-pass filter is also included in the variational formalism. A Green's function, derived for the Eular equation, is used to discuss the theoretical basis of the isotropic and anisotropic weighting factors.
The results obtained from the numerical variational analysis scheme suggest that the weights for the upstream and downstream observations should be of the same magnitude and as much as three times larger than the respective weights for the crosswind direction. These results were obtained by taking time t as a constant and considering a reasonable range of wind speeds. These suggestions seem to support the empirical anisotropic weighting factors proposed by Endlich and Mancuso. Additional discussion concerns weighting along the time coordinate simultaneously with the two space coordinates.
Abstract
The weighting factors used in conventional objective analysis methods are reviewed on the basis of numerical variational analysis. Special emphasis is placed on anisotropy (ellipticity) of the factors. The weighting factors of the objective analysis methods were empirically determined and are two dimensional in a horizontal plane (x, y). Most of these weighting factors are isotropic. However, anisotropic weighting factors have recently been used to give greater weight to the upstream and downstream observations as compared to those of the crosswind direction.
A simple advection equation is used as a dynamical constraint in the numerical variational analysis in order to take into account quantitatively the effect of wind direction and speed on the anisotropy. A simple low-pass filter is also included in the variational formalism. A Green's function, derived for the Eular equation, is used to discuss the theoretical basis of the isotropic and anisotropic weighting factors.
The results obtained from the numerical variational analysis scheme suggest that the weights for the upstream and downstream observations should be of the same magnitude and as much as three times larger than the respective weights for the crosswind direction. These results were obtained by taking time t as a constant and considering a reasonable range of wind speeds. These suggestions seem to support the empirical anisotropic weighting factors proposed by Endlich and Mancuso. Additional discussion concerns weighting along the time coordinate simultaneously with the two space coordinates.
Abstract
This study aims at the theoretical development of a method of “four-dimensional analysis,” namely the numerical variational analysis. The three basic types of variational formalism in the numerical variational analysis method are discussed. The basic formalisms are categorized into three areas: (1) “timewise localized” formalism, (2) formalism with strong constraint, and (3) formalism with weak constraint. Exact satisfaction of selected prognostic equations were formulated as constraints in the functionals for the first two formalisms. However, only the second formalism contains explicitly the time variation terms in the Euler equations. The third formalism is characterized by the subsidiary condition which requires that the prognostic or diagnostic equations must be approximately satisfied. The variational formalisms and the associated Euler-Lagrange equations are obtained in the form of finite-difference analogs. In this article, the filtering of cach formalism and the uniqueness of solutions of the Euler equations are discussed for a limit that time and space increments (Δt and Δx) approach zero. The results from the limited case study can be applied, with some modification, for the cases where these increments are finite. In addition, a numerical method of solving the Euler equations is discussed. The discussion is facilitated, merely for the sake of simplicity, by choosing a linear advection equation as a dynamical constraint. However, the discussion can be applied to more complicated and realistic cases.
Abstract
This study aims at the theoretical development of a method of “four-dimensional analysis,” namely the numerical variational analysis. The three basic types of variational formalism in the numerical variational analysis method are discussed. The basic formalisms are categorized into three areas: (1) “timewise localized” formalism, (2) formalism with strong constraint, and (3) formalism with weak constraint. Exact satisfaction of selected prognostic equations were formulated as constraints in the functionals for the first two formalisms. However, only the second formalism contains explicitly the time variation terms in the Euler equations. The third formalism is characterized by the subsidiary condition which requires that the prognostic or diagnostic equations must be approximately satisfied. The variational formalisms and the associated Euler-Lagrange equations are obtained in the form of finite-difference analogs. In this article, the filtering of cach formalism and the uniqueness of solutions of the Euler equations are discussed for a limit that time and space increments (Δt and Δx) approach zero. The results from the limited case study can be applied, with some modification, for the cases where these increments are finite. In addition, a numerical method of solving the Euler equations is discussed. The discussion is facilitated, merely for the sake of simplicity, by choosing a linear advection equation as a dynamical constraint. However, the discussion can be applied to more complicated and realistic cases.
Abstract
The “timewise localized” variational formalism of the numerical variational analysis method is used (1) to filter and suppress unnecessary high-frequency noises contained in initial and forecast fields and (2) to obtain dynamically sound initial values in the areas lacking data. A set of nonlinear longwave equations and a low-pass filter minimizing local changes are used in this paper as dynamical constraints. Also proposed in this study is a technique to assure the convergence of a numerical solution of the nonlinear Euler equations by an iterative process.
Three applications of the method are presented. The first two examples demonstrate that the initial guess in the iterative process influences significantly the speed of convergence. The last example is an application to the 500-mb analysis of hurricane Dora, 1964, and demonstrates a reasonable analysis in the data-sparse area where the hurricane was located at 1200 GMT on Sept. 8, 1964.
Abstract
The “timewise localized” variational formalism of the numerical variational analysis method is used (1) to filter and suppress unnecessary high-frequency noises contained in initial and forecast fields and (2) to obtain dynamically sound initial values in the areas lacking data. A set of nonlinear longwave equations and a low-pass filter minimizing local changes are used in this paper as dynamical constraints. Also proposed in this study is a technique to assure the convergence of a numerical solution of the nonlinear Euler equations by an iterative process.
Three applications of the method are presented. The first two examples demonstrate that the initial guess in the iterative process influences significantly the speed of convergence. The last example is an application to the 500-mb analysis of hurricane Dora, 1964, and demonstrates a reasonable analysis in the data-sparse area where the hurricane was located at 1200 GMT on Sept. 8, 1964.
Abstract
An investigation of the numerical variational analysis method is made for a case of “weak constraint” where the subsidiary condition is given in the form of an approximation. The simple example of a system moving with an optimized velocity is used to illustrate the theoretical development. The method is applied to analysis of the National Severe Storms Laboratory mesonetwork data of the severe storm gust that passed over the network on May 31, 1969.
Abstract
An investigation of the numerical variational analysis method is made for a case of “weak constraint” where the subsidiary condition is given in the form of an approximation. The simple example of a system moving with an optimized velocity is used to illustrate the theoretical development. The method is applied to analysis of the National Severe Storms Laboratory mesonetwork data of the severe storm gust that passed over the network on May 31, 1969.
Abstract
A technique for the objective analysis of air pollution based on the calculus of variations is described. Rather than find a system of diffusion coefficients which best fit a source inventory and receptor sampling, a series of hypothetical sources and a background contamination are optimized to best fit the receptor sampling and the diffusion model applied. The advantage of this approach is that no source inventory is necessary. A low-pass filter is described which removes small-scale phenomena from the resulting ensemble of optimized plumes and adjusts the analyzed patterns to better fit the input air quality data. These methods are applied to SO2 data in the vicinity of a zinc smelter at Blackwell in north-central Oklahoma. The resulting objective analyses demonstrate that reasonable patterns of contamination can be extrapolated from sparse air quality data through the use of this technique.
Abstract
A technique for the objective analysis of air pollution based on the calculus of variations is described. Rather than find a system of diffusion coefficients which best fit a source inventory and receptor sampling, a series of hypothetical sources and a background contamination are optimized to best fit the receptor sampling and the diffusion model applied. The advantage of this approach is that no source inventory is necessary. A low-pass filter is described which removes small-scale phenomena from the resulting ensemble of optimized plumes and adjusts the analyzed patterns to better fit the input air quality data. These methods are applied to SO2 data in the vicinity of a zinc smelter at Blackwell in north-central Oklahoma. The resulting objective analyses demonstrate that reasonable patterns of contamination can be extrapolated from sparse air quality data through the use of this technique.
Abstract
The effects of background baroclinic zonal flow and bottom pressure decoupling on midlatitude oceanic Rossby wave dynamics using a high-resolution OGCM simulation are investigated. To examine these effects, the phase speed and vertical structure of the simulated wave are compared with each of the different linear Rossby wave solutions obtained for two different circumstances (with or without background flow) and two different boundary conditions (a flat bottom or a bottom pressure decoupling condition). First, a frequency–wavenumber spectrum is examined for depth anomaly of the permanent thermocline (27.0σθ surface) along 32°S. Most of the energy is distributed along the theoretical dispersion curve including the effects of background flow and bottom pressure decoupling. The authors focus on a secondary dominant peak (appearing at a frequency greater than 1 cycle per year) at which the differences between the dispersion curves are large enough to discuss the relation between the spectral peak and the dispersion curves. The phase speed of this peak is nearly 1.5 times larger than that of the standard long-wave theory (flat bottom and no background flow), which is similar to results from previous observational studies. The extended long-wave theory including background flow and bottom pressure decoupling effects overestimates the phase speed. However, taking into account finite wavelength effects, this theory provides a phase speed much closer to that of the secondary dominant peak. The vertical structure corresponding to the wave of the secondary dominant peak extracted by composite analysis is intensified in the surface layer, a result similar to that from the theory including background flow and bottom pressure decoupling effects. The authors also compare the latitudinal distribution of midlatitude phase speed estimated by the frequency–wavenumber spectrum with theoretical results. The theory including background flow, bottom pressure decoupling, and finite wavelength effects reproduces the latitudinal distribution well, suggesting that these effects are important for explaining Rossby wave speed. The dominant factor enhancing the phase speed is bottom pressure decoupling related to rough bottom topography, while north of 30°N the background flow makes a strong contribution to the phase speed enhancement.
Abstract
The effects of background baroclinic zonal flow and bottom pressure decoupling on midlatitude oceanic Rossby wave dynamics using a high-resolution OGCM simulation are investigated. To examine these effects, the phase speed and vertical structure of the simulated wave are compared with each of the different linear Rossby wave solutions obtained for two different circumstances (with or without background flow) and two different boundary conditions (a flat bottom or a bottom pressure decoupling condition). First, a frequency–wavenumber spectrum is examined for depth anomaly of the permanent thermocline (27.0σθ surface) along 32°S. Most of the energy is distributed along the theoretical dispersion curve including the effects of background flow and bottom pressure decoupling. The authors focus on a secondary dominant peak (appearing at a frequency greater than 1 cycle per year) at which the differences between the dispersion curves are large enough to discuss the relation between the spectral peak and the dispersion curves. The phase speed of this peak is nearly 1.5 times larger than that of the standard long-wave theory (flat bottom and no background flow), which is similar to results from previous observational studies. The extended long-wave theory including background flow and bottom pressure decoupling effects overestimates the phase speed. However, taking into account finite wavelength effects, this theory provides a phase speed much closer to that of the secondary dominant peak. The vertical structure corresponding to the wave of the secondary dominant peak extracted by composite analysis is intensified in the surface layer, a result similar to that from the theory including background flow and bottom pressure decoupling effects. The authors also compare the latitudinal distribution of midlatitude phase speed estimated by the frequency–wavenumber spectrum with theoretical results. The theory including background flow, bottom pressure decoupling, and finite wavelength effects reproduces the latitudinal distribution well, suggesting that these effects are important for explaining Rossby wave speed. The dominant factor enhancing the phase speed is bottom pressure decoupling related to rough bottom topography, while north of 30°N the background flow makes a strong contribution to the phase speed enhancement.
Abstract
Located at the center of the western North Pacific Subtropical Gyre, the Subtropical Countercurrent (STCC) is not only abundant in mesoscale eddies, but also exhibits prominent submesoscale eddy features. Output from a 
Abstract
Located at the center of the western North Pacific Subtropical Gyre, the Subtropical Countercurrent (STCC) is not only abundant in mesoscale eddies, but also exhibits prominent submesoscale eddy features. Output from a
Abstract
The purpose of this research is to investigate, by means of numerical simulation experiments, the complex interactions between consecutive toroidally circulating buoyant elements (thermals) when these occur in either rotating or nonrotating environments. The study includes both the vortex formation process and the effect that this process has on the properties of the one or more buoyant elements involved in the interaction.
A numerical model of a self-developing thermal of the Ogura type was modified to include tangential accelerations and a provision for injecting a second thermal into the field of a previous one. Computer outputs are obtained at several times during the evolution of both solitary thermals and two types of successive thermals, released at intervals of 2 and 7 min. These were also performed for three different magnitudes of pre-existing vorticity, comparable to magnitudes measured in the vicinity of thunderstorms. The results of the complex interactions are illustrated in the patterns of isotherms, stream functions, and velocity isotachs.
A thermal is accelerated in circulation and velocity of rise upon encountering the wake of a previous thermal, and velocity enhancements can be quite spectacular. A rotation field causes both solitary and successive thermals to surrender part of their kinetic energy to vortex formation, but lateral confinement of the thermal slows the mixing and reduces the heat loss. The first effect tends to suppress the vertical momentum of the thermal, and the second one tends to enhance it. Nevertheless, all but one of the solitary and successive thermals investigated were suppressed by the vortex formation interaction; this one, a second thermal with a 7-min interval, appears to represent an optimum combination of buoyancy and ambient vorticity, since it forms a more intense vortex and simultaneously maintains the strongest vertical velocity for one particular magnitude of ambient vorticity. When the rotation rate initially is very large, on the other hand, a solitary thermal is “dominated” by the rotation field, and neither forms a strong vortex nor develops the usual characteristics of a vigorous thermal.
The results show several features of the numerical simulation to be in agreement with solitary and successive thermals simulated in the laboratory. Some possible recognition features are suggested for the detection of situations where strong interactions occur between a buoyant element and the ambient vorticity field. Some of the results must be applicable to atmospheric convection. The computations relating to vortex formation must be considered relevant to tornadoes, despite the shallow depth used for the convection layer.
Abstract
The purpose of this research is to investigate, by means of numerical simulation experiments, the complex interactions between consecutive toroidally circulating buoyant elements (thermals) when these occur in either rotating or nonrotating environments. The study includes both the vortex formation process and the effect that this process has on the properties of the one or more buoyant elements involved in the interaction.
A numerical model of a self-developing thermal of the Ogura type was modified to include tangential accelerations and a provision for injecting a second thermal into the field of a previous one. Computer outputs are obtained at several times during the evolution of both solitary thermals and two types of successive thermals, released at intervals of 2 and 7 min. These were also performed for three different magnitudes of pre-existing vorticity, comparable to magnitudes measured in the vicinity of thunderstorms. The results of the complex interactions are illustrated in the patterns of isotherms, stream functions, and velocity isotachs.
A thermal is accelerated in circulation and velocity of rise upon encountering the wake of a previous thermal, and velocity enhancements can be quite spectacular. A rotation field causes both solitary and successive thermals to surrender part of their kinetic energy to vortex formation, but lateral confinement of the thermal slows the mixing and reduces the heat loss. The first effect tends to suppress the vertical momentum of the thermal, and the second one tends to enhance it. Nevertheless, all but one of the solitary and successive thermals investigated were suppressed by the vortex formation interaction; this one, a second thermal with a 7-min interval, appears to represent an optimum combination of buoyancy and ambient vorticity, since it forms a more intense vortex and simultaneously maintains the strongest vertical velocity for one particular magnitude of ambient vorticity. When the rotation rate initially is very large, on the other hand, a solitary thermal is “dominated” by the rotation field, and neither forms a strong vortex nor develops the usual characteristics of a vigorous thermal.
The results show several features of the numerical simulation to be in agreement with solitary and successive thermals simulated in the laboratory. Some possible recognition features are suggested for the detection of situations where strong interactions occur between a buoyant element and the ambient vorticity field. Some of the results must be applicable to atmospheric convection. The computations relating to vortex formation must be considered relevant to tornadoes, despite the shallow depth used for the convection layer.
Abstract
Solitary thermals and continuous plume thermals both occur in nature, and the intermediate case of interacting successive thermals in a series may also be an important part of atmospheric convection. This analysis shows that residual updraft and vorticity concentration in the wake of a preceding thermal can have important effects on its successor.
A fluid mechanics model of buoyant clouds rising through a rotating medium is constructed for the purpose of predicting some of the sequential thermal effects that can be measured quantitatively for thermals simulated in the laboratory. The agreement with theory is satisfactory for the parameters that are subject to measurement, but some relevant constants can only be determined experimentally.
For a situation in which a first thermal reacts strongly with the rotation field, it is shown that a succeeding thermal may receive a sizable enhancement of its vertical momentum even though its predecessor was suppressed by the interaction. These findings may be relevant to the generation and maintenance of small-scale atmospheric vortexes such as tornadoes, waterspouts, and dust devils.
Abstract
Solitary thermals and continuous plume thermals both occur in nature, and the intermediate case of interacting successive thermals in a series may also be an important part of atmospheric convection. This analysis shows that residual updraft and vorticity concentration in the wake of a preceding thermal can have important effects on its successor.
A fluid mechanics model of buoyant clouds rising through a rotating medium is constructed for the purpose of predicting some of the sequential thermal effects that can be measured quantitatively for thermals simulated in the laboratory. The agreement with theory is satisfactory for the parameters that are subject to measurement, but some relevant constants can only be determined experimentally.
For a situation in which a first thermal reacts strongly with the rotation field, it is shown that a succeeding thermal may receive a sizable enhancement of its vertical momentum even though its predecessor was suppressed by the interaction. These findings may be relevant to the generation and maintenance of small-scale atmospheric vortexes such as tornadoes, waterspouts, and dust devils.
