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- Author or Editor: Alexander E. MacDonald x
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Abstract
The atmosphere is idealized into two kinematic steady states. The first, common in the earth's atmosphere, is rotational and quasi‐nondivergent; the second is divergent and quasi‐irrotational (with respect to space). A motion parameter is introduced which reveals a symmetry between these two types of steady state. When the motion parameter is positive, a rotational steady state is possible, with the absolute vorticity given by the square root of the motion parameter and the divergence equal to zero. When the motion parameter is negative, a divergent steady state is possible, with the divergence given by the square root of the negative of the motion parameter and the absolute vorticity equal to zero.
An observational study using objectively analyzed data reveals that synoptic-scale areas with negative motion parameter, large divergence and small absolute vorticity are 1) common in the subtropical upper troposphere during summer, 2) are generally associated with heavy wet convection, 3) have a mean geographical location which is similar to that of the large upper tropospheric continental anticyclones, and 4) exist in the upper troposphere in conjunction with a tropical storm and some large tornado outbreaks.
Abstract
The atmosphere is idealized into two kinematic steady states. The first, common in the earth's atmosphere, is rotational and quasi‐nondivergent; the second is divergent and quasi‐irrotational (with respect to space). A motion parameter is introduced which reveals a symmetry between these two types of steady state. When the motion parameter is positive, a rotational steady state is possible, with the absolute vorticity given by the square root of the motion parameter and the divergence equal to zero. When the motion parameter is negative, a divergent steady state is possible, with the divergence given by the square root of the negative of the motion parameter and the absolute vorticity equal to zero.
An observational study using objectively analyzed data reveals that synoptic-scale areas with negative motion parameter, large divergence and small absolute vorticity are 1) common in the subtropical upper troposphere during summer, 2) are generally associated with heavy wet convection, 3) have a mean geographical location which is similar to that of the large upper tropospheric continental anticyclones, and 4) exist in the upper troposphere in conjunction with a tropical storm and some large tornado outbreaks.
Abstract
Two sets of initial conditions are used to integrate a three-level quasi-geostrophic model in spectral form. After a maximum perturbation kinetic energy is reached, a barotropic exchange in established between the zonal flow and the perturbation with an apparent periodicity from 2 to 4 days. The initial state includes a finite amplitude baroclinic mode which is highly unstable in the linear sense. This mode exhibits a negative growth rate for about the first two days of the integration due to barotropic exchanges with other modes. Spectra of kinetic and available potential energies, enstrophy, and omega2 are presented. The kinetic and available energy display a –3 slope for intermediate, scales for the initial integration period when perturbation kinetic energy is actively growing at the expense of the mean flow available energy. The effect of the variation of stratification with height, dissipation, heating, mountains, and truncation of the spectral system is discussed.
Abstract
Two sets of initial conditions are used to integrate a three-level quasi-geostrophic model in spectral form. After a maximum perturbation kinetic energy is reached, a barotropic exchange in established between the zonal flow and the perturbation with an apparent periodicity from 2 to 4 days. The initial state includes a finite amplitude baroclinic mode which is highly unstable in the linear sense. This mode exhibits a negative growth rate for about the first two days of the integration due to barotropic exchanges with other modes. Spectra of kinetic and available potential energies, enstrophy, and omega2 are presented. The kinetic and available energy display a –3 slope for intermediate, scales for the initial integration period when perturbation kinetic energy is actively growing at the expense of the mean flow available energy. The effect of the variation of stratification with height, dissipation, heating, mountains, and truncation of the spectral system is discussed.
Abstract
An icosahedral-hexagonal shallow-water model (SWM) on the sphere is formulated on a local Cartesian coordinate based on the general stereographic projection plane. It is discretized with the third-order Adam–Bashforth time-differencing scheme and the second-order finite-volume operators for spatial derivative terms. The finite-volume operators are applied to the model variables defined on the nonstaggered grid with the edge variables interpolated using polynomial interpolation. The projected local coordinate reduces the solution space from the three-dimensional, curved, spherical surface to the two-dimensional plane and thus reduces the number of complete sets of basis functions in the Vandermonde matrix, which is the essential component of the interpolation. The use of a local Cartesian coordinate also greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. The SWM is evaluated with the standard test cases of Williamson et al. Numerical results show that the icosahedral SWM is free from Pole problems. The SWM is a second-order finite-volume model as shown by the truncation error convergence test. The lee-wave numerical solutions are compared and found to be very similar to the solutions shown in other SWMs. The SWM is stably integrated for several weeks without numerical dissipation using the wavenumber 4 Rossby–Haurwitz solution as an initial condition. It is also shown that the icosahedral SWM achieves mass conservation within round-off errors as one would expect from a finite-volume model.
Abstract
An icosahedral-hexagonal shallow-water model (SWM) on the sphere is formulated on a local Cartesian coordinate based on the general stereographic projection plane. It is discretized with the third-order Adam–Bashforth time-differencing scheme and the second-order finite-volume operators for spatial derivative terms. The finite-volume operators are applied to the model variables defined on the nonstaggered grid with the edge variables interpolated using polynomial interpolation. The projected local coordinate reduces the solution space from the three-dimensional, curved, spherical surface to the two-dimensional plane and thus reduces the number of complete sets of basis functions in the Vandermonde matrix, which is the essential component of the interpolation. The use of a local Cartesian coordinate also greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. The SWM is evaluated with the standard test cases of Williamson et al. Numerical results show that the icosahedral SWM is free from Pole problems. The SWM is a second-order finite-volume model as shown by the truncation error convergence test. The lee-wave numerical solutions are compared and found to be very similar to the solutions shown in other SWMs. The SWM is stably integrated for several weeks without numerical dissipation using the wavenumber 4 Rossby–Haurwitz solution as an initial condition. It is also shown that the icosahedral SWM achieves mass conservation within round-off errors as one would expect from a finite-volume model.
Abstract
In recent years techniques have been developed to obtain integrated water vapor along slant paths between ground-based Global Positioning System (GPS) receivers and the GPS satellites. Results are presented of an observing system simulation (OSS) to determine whether three-dimensional water vapor fields could be recovered from a high-resolution network (e.g., with 40-km spacing) of GPS receivers, in combination with surface moisture observations and a limited number of moisture soundings. The paper describes a three-dimensional variational analysis (3DVAR) that recovers the moisture field from the slant integrated water vapor and other observations. Comparisons between “nature” moisture fields taken from mesoscale models and fields recovered using 3DVAR are presented. It is concluded that a high-resolution network of GPS receivers may allow diagnosis of three-dimensional water vapor, with applications for both positioning and mesoscale weather prediction.
Abstract
In recent years techniques have been developed to obtain integrated water vapor along slant paths between ground-based Global Positioning System (GPS) receivers and the GPS satellites. Results are presented of an observing system simulation (OSS) to determine whether three-dimensional water vapor fields could be recovered from a high-resolution network (e.g., with 40-km spacing) of GPS receivers, in combination with surface moisture observations and a limited number of moisture soundings. The paper describes a three-dimensional variational analysis (3DVAR) that recovers the moisture field from the slant integrated water vapor and other observations. Comparisons between “nature” moisture fields taken from mesoscale models and fields recovered using 3DVAR are presented. It is concluded that a high-resolution network of GPS receivers may allow diagnosis of three-dimensional water vapor, with applications for both positioning and mesoscale weather prediction.
Abstract
This article is one in a series describing the functionality of the Flow-Following, Finite-Volume Icosahedral Model (FIM) developed at NOAA’s Earth System Research Laboratory. Emphasis in this article is on the design of the vertical coordinate—the “flow following” aspect of FIM. The coordinate is terrain-following near the ground and isentropic in the free atmosphere. The spatial transition between the two coordinates is adaptive and is based on the arbitrary Lagrangian–Eulerian (ALE) paradigm. The impact of vertical resolution trade-offs between the present hybrid approach and traditional terrain-following coordinates is demonstrated in a three-part case study.
Abstract
This article is one in a series describing the functionality of the Flow-Following, Finite-Volume Icosahedral Model (FIM) developed at NOAA’s Earth System Research Laboratory. Emphasis in this article is on the design of the vertical coordinate—the “flow following” aspect of FIM. The coordinate is terrain-following near the ground and isentropic in the free atmosphere. The spatial transition between the two coordinates is adaptive and is based on the arbitrary Lagrangian–Eulerian (ALE) paradigm. The impact of vertical resolution trade-offs between the present hybrid approach and traditional terrain-following coordinates is demonstrated in a three-part case study.
Abstract
A hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrain-following/isentropic vertical coordinate is described. The model is an extension to three spatial dimensions of a previously developed, icosahedral, shallow-water model featuring user-selectable horizontal resolution and employing indirect addressing techniques. The vertical grid is adaptive to maximize the portion of the atmosphere mapped into the isentropic coordinate subdomain. The model, best described as a stacked shallow-water model, is being tested extensively on real-time medium-range forecasts to ready it for possible inclusion in operational multimodel ensembles for medium-range to seasonal prediction.
Abstract
A hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrain-following/isentropic vertical coordinate is described. The model is an extension to three spatial dimensions of a previously developed, icosahedral, shallow-water model featuring user-selectable horizontal resolution and employing indirect addressing techniques. The vertical grid is adaptive to maximize the portion of the atmosphere mapped into the isentropic coordinate subdomain. The model, best described as a stacked shallow-water model, is being tested extensively on real-time medium-range forecasts to ready it for possible inclusion in operational multimodel ensembles for medium-range to seasonal prediction.
