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Abstract
We describe the development and preliminary testing of a numerical scheme designed to predict the global circulation which can also telescope into local subdomains of enhanced vertical and horizontal resolution. The accuracy of the method appears intermediate to the accuracy of purely spectral and grid point models, but it is especially well suited to study certain practical predictability problems within limited area domains. The approach is based upon separate Galerkin approximations in longitude and latitude. The longitude variation is discretized in terms of truncated Fourier series, while the latitude structure of the Fourier amplitudes is depicted as sums of piecewise continuous linear functions (finite elements). The vertical structure is also described in terms of finite elements. The technique is especially well suited to fine resolution of polar caps within which a given wavenumber truncation ensures enhanced local resolution in longitude, and where a refined element size can also be implemented to improve latitude resolution. These polar lenses can be rotated over any geographical region of special interest and therefore serve to enhance local resolution in subdomains that have completely general two-way interactions with global scales. The numerical difficulties generally associated with polar singularities do not pose special problems in the present approach. This is illustrated with a series of Rossby-Haurwitz wave examples Cases with divergent flow and multilevel applications each require certain additional modifications of the horizontal treatment.
The multilevel version has a fully interactive atmosphere, interface, and subsurface. The vertical fluxes throughout the atmospheric portion of the model are formulated in terms of a turbulence closure which explicitly predicts evolution of the troposphere, the planetary boundary layer, and the surface boundary layer. Surface turbulent fluxes are computed as the flux that naturally appears at the lowest level of the model, without separate parameterization in terms of bulk transfer coefficients. The sensitivity of these calculations to vertical resolution and to the frequency of updating the infrared flux is described. It appears that as few as three appropriately positioned forecast levels in the surface and planetary boundary layers may be sufficient to many applications. The principal deficiencies of the approach are the relative complexity introduced by the mixed numerical treatment and a rather high computational overhead. However, the method is especially well suited to address questions of regional predictability in which limited area models have produced rather perplexing results that may be partly attributable to artificial lateral boundaries. A preliminary study of this is made for the case of topographically bound low-level jets.
Abstract
We describe the development and preliminary testing of a numerical scheme designed to predict the global circulation which can also telescope into local subdomains of enhanced vertical and horizontal resolution. The accuracy of the method appears intermediate to the accuracy of purely spectral and grid point models, but it is especially well suited to study certain practical predictability problems within limited area domains. The approach is based upon separate Galerkin approximations in longitude and latitude. The longitude variation is discretized in terms of truncated Fourier series, while the latitude structure of the Fourier amplitudes is depicted as sums of piecewise continuous linear functions (finite elements). The vertical structure is also described in terms of finite elements. The technique is especially well suited to fine resolution of polar caps within which a given wavenumber truncation ensures enhanced local resolution in longitude, and where a refined element size can also be implemented to improve latitude resolution. These polar lenses can be rotated over any geographical region of special interest and therefore serve to enhance local resolution in subdomains that have completely general two-way interactions with global scales. The numerical difficulties generally associated with polar singularities do not pose special problems in the present approach. This is illustrated with a series of Rossby-Haurwitz wave examples Cases with divergent flow and multilevel applications each require certain additional modifications of the horizontal treatment.
The multilevel version has a fully interactive atmosphere, interface, and subsurface. The vertical fluxes throughout the atmospheric portion of the model are formulated in terms of a turbulence closure which explicitly predicts evolution of the troposphere, the planetary boundary layer, and the surface boundary layer. Surface turbulent fluxes are computed as the flux that naturally appears at the lowest level of the model, without separate parameterization in terms of bulk transfer coefficients. The sensitivity of these calculations to vertical resolution and to the frequency of updating the infrared flux is described. It appears that as few as three appropriately positioned forecast levels in the surface and planetary boundary layers may be sufficient to many applications. The principal deficiencies of the approach are the relative complexity introduced by the mixed numerical treatment and a rather high computational overhead. However, the method is especially well suited to address questions of regional predictability in which limited area models have produced rather perplexing results that may be partly attributable to artificial lateral boundaries. A preliminary study of this is made for the case of topographically bound low-level jets.
Abstract
A linearized model of forced Boussinesq, hydrostatic, gravity inertia waves is developed in a terrain-following coordinate system. Diurnally periodic motions, forced by diurnally fluctuating buoyancy forces above sloping terrain, are studied through particular solutions that represent bounds to the complete solutions. The present results suggest that gently sloping terrains exert important controls on convective activity through boundary layer convergence generation. The model solutions appear to he most sensitive to details of the diurnally oscillating thermal boundary layer. They are also rather sensitive to synoptic-scale ambient circulations as well as dissipation, but apparently less sensitive to horizontal variations of stratification.
Abstract
A linearized model of forced Boussinesq, hydrostatic, gravity inertia waves is developed in a terrain-following coordinate system. Diurnally periodic motions, forced by diurnally fluctuating buoyancy forces above sloping terrain, are studied through particular solutions that represent bounds to the complete solutions. The present results suggest that gently sloping terrains exert important controls on convective activity through boundary layer convergence generation. The model solutions appear to he most sensitive to details of the diurnally oscillating thermal boundary layer. They are also rather sensitive to synoptic-scale ambient circulations as well as dissipation, but apparently less sensitive to horizontal variations of stratification.
Abstract
The transient adjustment of the baroclinic structure of a warm core disturbance forced by heating is studied as an initial value problem. It is found that the divergent flow in convective regions adjusts on a time scale of a few hours, and the surrounding divergence field outward to about 2000 km adjusts on a time scale of about 1 day. This rapid adjustment is due to the outward radiation of gravity inertia waves. The adjustment is sufficiently rapid that diurnally periodic forcings produce divergence fields that are almost in phase, and in practically instantaneous equilibrium with the forcings.
In the case of latent heating associated with local precipitation rates in excess of a few centimeters per day, the strongly anticyclonic upper tropospheric pressure field may render the balance equation non-elliptic. When they occur in the tropics, isolated events of this magnitude can produce cross-isobaric flows on the order of 1 m s−1 outward to beyond 2000 km. A plausible influence of these tropical flows upon midlatitudes is hypothesized, following the argument in a climatological study by Blackmon et al. (1977). The present results suggest that the mechanism in question can act on time scales as short as one or two days after the inception of a strong tropical disturbance.
Abstract
The transient adjustment of the baroclinic structure of a warm core disturbance forced by heating is studied as an initial value problem. It is found that the divergent flow in convective regions adjusts on a time scale of a few hours, and the surrounding divergence field outward to about 2000 km adjusts on a time scale of about 1 day. This rapid adjustment is due to the outward radiation of gravity inertia waves. The adjustment is sufficiently rapid that diurnally periodic forcings produce divergence fields that are almost in phase, and in practically instantaneous equilibrium with the forcings.
In the case of latent heating associated with local precipitation rates in excess of a few centimeters per day, the strongly anticyclonic upper tropospheric pressure field may render the balance equation non-elliptic. When they occur in the tropics, isolated events of this magnitude can produce cross-isobaric flows on the order of 1 m s−1 outward to beyond 2000 km. A plausible influence of these tropical flows upon midlatitudes is hypothesized, following the argument in a climatological study by Blackmon et al. (1977). The present results suggest that the mechanism in question can act on time scales as short as one or two days after the inception of a strong tropical disturbance.
Abstract
The effect of friction in strongly divergent steady flows is studied. It is found that friction weakens flow divergence out of strong high-pressure centers, contrary to the more commonly studied case for weaker high-pressure centers in rotating flows, for which friction produces divergence. The stability of the solution is discussed for the general case on a linear basis. Nonlinear analytic solutions are presented for the case of no deformation in the flow. The conclusions are quantified in a drag, deformation and Laplacian of geopotential parameter space.
Abstract
The effect of friction in strongly divergent steady flows is studied. It is found that friction weakens flow divergence out of strong high-pressure centers, contrary to the more commonly studied case for weaker high-pressure centers in rotating flows, for which friction produces divergence. The stability of the solution is discussed for the general case on a linear basis. Nonlinear analytic solutions are presented for the case of no deformation in the flow. The conclusions are quantified in a drag, deformation and Laplacian of geopotential parameter space.
Abstract
The influence of one-way interacting lateral bounday conditions upon the predictability of flows in boundeddomains is studied using the barotropic nondivergent model in global and local domains. Past studies haveattempted to reconcile the apparent contradiction between pessimistic forecast of predictability theory and thehigh predictability actually found in regional models. Those investigations have emphasized the rather differentspectra and forcing mechanisms that are not considered in the theoretical estimates. We demonstrate that thepredictability remains high in an unforced, inertially driven local flow characterized by a typical synoptic scalespectrum, and constrained only by lateral boundary specification. We also offer a possible reconciliation ofthese results with the classical theory. It is shown that one-way interacting boundary conditions enhance thepredictability of flow in a local region which, without the boundary constraints, has limited predictabifity. Thedegree of this boundary constraint is dependent on the size of the domain, on the nature of flow in the domainand on the scale structure of the error field. The boundary constraint is particularly strong when a substantialportion of the larger scale flow in the domain is imposed through the boundary condition. In that case, smallscale initial uncertainties have limited interaction with the basic flow field because of scale separation andbecause the largest scales in the domain do not react to internal dynamics.
Abstract
The influence of one-way interacting lateral bounday conditions upon the predictability of flows in boundeddomains is studied using the barotropic nondivergent model in global and local domains. Past studies haveattempted to reconcile the apparent contradiction between pessimistic forecast of predictability theory and thehigh predictability actually found in regional models. Those investigations have emphasized the rather differentspectra and forcing mechanisms that are not considered in the theoretical estimates. We demonstrate that thepredictability remains high in an unforced, inertially driven local flow characterized by a typical synoptic scalespectrum, and constrained only by lateral boundary specification. We also offer a possible reconciliation ofthese results with the classical theory. It is shown that one-way interacting boundary conditions enhance thepredictability of flow in a local region which, without the boundary constraints, has limited predictabifity. Thedegree of this boundary constraint is dependent on the size of the domain, on the nature of flow in the domainand on the scale structure of the error field. The boundary constraint is particularly strong when a substantialportion of the larger scale flow in the domain is imposed through the boundary condition. In that case, smallscale initial uncertainties have limited interaction with the basic flow field because of scale separation andbecause the largest scales in the domain do not react to internal dynamics.
Abstract
One year of geopotential data obtained from the National Meteorological Center and the National Center for Atmospheric Research are diagnosed for the occurrence of non-elliptic regions with respect to the balance equation. The highest frequencies of such occurrences appear at 200 mb over the subtropical oceans where there are few radiosonde observations. Substantial 200 mb frequencies are also found over the United States in the summer season above a reliable data net. A diagnosis of flow divergence implied for the non-elliptic data by a theoretical analysis of Paegle and Paegle (1974) produces values greatly in excess of. typical observations. This suggests that the gridding of the data by objective analysis may not have been adequate and/or that the aforementioned theory overestimates flow divergence in these regions. It is likely that non-elliptic data are important for initialization of primitive equation forecast models. It may be inferred that greater data accuracy, as well as better initialization techniques within non-elliptic regions, are required.
Abstract
One year of geopotential data obtained from the National Meteorological Center and the National Center for Atmospheric Research are diagnosed for the occurrence of non-elliptic regions with respect to the balance equation. The highest frequencies of such occurrences appear at 200 mb over the subtropical oceans where there are few radiosonde observations. Substantial 200 mb frequencies are also found over the United States in the summer season above a reliable data net. A diagnosis of flow divergence implied for the non-elliptic data by a theoretical analysis of Paegle and Paegle (1974) produces values greatly in excess of. typical observations. This suggests that the gridding of the data by objective analysis may not have been adequate and/or that the aforementioned theory overestimates flow divergence in these regions. It is likely that non-elliptic data are important for initialization of primitive equation forecast models. It may be inferred that greater data accuracy, as well as better initialization techniques within non-elliptic regions, are required.
Abstract
Observed perturbation kinetic and available energy are presented for a region about 3000 km on a side to study the horizontal homogeneity and general characteristics of geostrophic motions. Frequency spectral analysis is used to determine the dependence of these characteristics on time scales. For all time scales considered the perturbation energies display horizontal inhomogeneities, but these are less pronounced for shorter time scales. For time scales smaller than 4 days the spectra of horizontal kinetic and available potential energies decrease with increasing frequency, and approximately fit power laws with exponents between −2 to −3.5, depending on location. The frequency spectra for geostrophic vertical velocities are markedly different for different climatic locations. The frequency spectra are related to one-dimensional wavenumber spectra by introducing suitable transformation of variables. The results obtained for the higher end of these spectra are interpreted in terms of those predicted by Charney for quasi-geostrophic turbulence.
Abstract
Observed perturbation kinetic and available energy are presented for a region about 3000 km on a side to study the horizontal homogeneity and general characteristics of geostrophic motions. Frequency spectral analysis is used to determine the dependence of these characteristics on time scales. For all time scales considered the perturbation energies display horizontal inhomogeneities, but these are less pronounced for shorter time scales. For time scales smaller than 4 days the spectra of horizontal kinetic and available potential energies decrease with increasing frequency, and approximately fit power laws with exponents between −2 to −3.5, depending on location. The frequency spectra for geostrophic vertical velocities are markedly different for different climatic locations. The frequency spectra are related to one-dimensional wavenumber spectra by introducing suitable transformation of variables. The results obtained for the higher end of these spectra are interpreted in terms of those predicted by Charney for quasi-geostrophic turbulence.
Abstract
An efficient alternative to the customary balance equation solution procedures is described which gives very similar solutions for those cases when the balance equation is elliptic. This alternative invokes some assumptions that are not usually applied to the nonlinear balance equation, but which are justified by comparisons with the standard solutions to the balance equation in both rectangular and spherical geometries. The solution tends toward a flow with zero absolute vorticity as the pressure field tends toward configurations for which the balance equation is non-elliptic. Such non-elliptic pressure fields correspond to force fields with sufficient positive divergence with respect to space to generate flow divergence. In this case a non-divergent balanced solution may not exist, and is physically meaningless if it does exist, but a reasonable divergent balanced solution can be obtained by the proposed technique.
Abstract
An efficient alternative to the customary balance equation solution procedures is described which gives very similar solutions for those cases when the balance equation is elliptic. This alternative invokes some assumptions that are not usually applied to the nonlinear balance equation, but which are justified by comparisons with the standard solutions to the balance equation in both rectangular and spherical geometries. The solution tends toward a flow with zero absolute vorticity as the pressure field tends toward configurations for which the balance equation is non-elliptic. Such non-elliptic pressure fields correspond to force fields with sufficient positive divergence with respect to space to generate flow divergence. In this case a non-divergent balanced solution may not exist, and is physically meaningless if it does exist, but a reasonable divergent balanced solution can be obtained by the proposed technique.
Abstract
Time-dependent flow solutions for steady supergradient pressure patterns are presented for a variety of initial flow configurations. These solutions discriminate initial conditions and pressure patterns that produce stable and unstable flow evolutions. It is shown that steady-state divergent flows are realizable for commonly observed pressure patterns of the upper troposphere. In these cases, the steady state is approached on relatively short time scales. Solutions agree roughly with observed features of atmospheric flows and constitute a plausible explanation for strong upper level outflows.
Abstract
Time-dependent flow solutions for steady supergradient pressure patterns are presented for a variety of initial flow configurations. These solutions discriminate initial conditions and pressure patterns that produce stable and unstable flow evolutions. It is shown that steady-state divergent flows are realizable for commonly observed pressure patterns of the upper troposphere. In these cases, the steady state is approached on relatively short time scales. Solutions agree roughly with observed features of atmospheric flows and constitute a plausible explanation for strong upper level outflows.
