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Abstract
Through analysis of the spectra of a Dirac delta function the notion of believable and unbelievable scales in a spectral transform model is quantified. The smallest resolved local features are shown to have an average wavenumber a factor of
Abstract
Through analysis of the spectra of a Dirac delta function the notion of believable and unbelievable scales in a spectral transform model is quantified. The smallest resolved local features are shown to have an average wavenumber a factor of
Abstract
In this paper a simple 2D linear quasigeostrophic model is used to investigate how the development of local confined cyclonic perturbations is dependent on the perturbation scale, location, and tilt in Eady-type basic states. It is found that the initial growth of the perturbation can be maximized by reducing both the vertical and horizontal scale and using a “midtropospheric” vertical location. “Potential vorticity (PV) thinking” suggests the concept of “PV unshielding” to explain this result. Adding a meridional gradient of basic-state PV lowers the vertical location of perturbations that optimally excite sustained growth. This can be understood by considering the behavior of the upward and downward propagating parts of the initial perturbation. It is found that the importance of the initial perturbation tilt is diminished for confined perturbations. It is shown that diabatic heating in a vertically confined region can lead to a perturbation that exhibits rapid growth. The findings in this paper lay some foundations for understanding calculated optimal growth structures, such as the singular vectors produced routinely by the European Centre for Medium-Range Weather Forecasts.
Abstract
In this paper a simple 2D linear quasigeostrophic model is used to investigate how the development of local confined cyclonic perturbations is dependent on the perturbation scale, location, and tilt in Eady-type basic states. It is found that the initial growth of the perturbation can be maximized by reducing both the vertical and horizontal scale and using a “midtropospheric” vertical location. “Potential vorticity (PV) thinking” suggests the concept of “PV unshielding” to explain this result. Adding a meridional gradient of basic-state PV lowers the vertical location of perturbations that optimally excite sustained growth. This can be understood by considering the behavior of the upward and downward propagating parts of the initial perturbation. It is found that the importance of the initial perturbation tilt is diminished for confined perturbations. It is shown that diabatic heating in a vertically confined region can lead to a perturbation that exhibits rapid growth. The findings in this paper lay some foundations for understanding calculated optimal growth structures, such as the singular vectors produced routinely by the European Centre for Medium-Range Weather Forecasts.
Abstract
Baroclinic instability calculations published by Gall are repeated using the model developed by the authors for use in their own stability studies. Results indicate that some of the differences in the wavelength of maximum linear growth rate found previously may be accounted for by differences in flow profile, but there remains a discrepancy which is a likely consequence of either truncation error in Gall's calculations or a coding error in one or the other model (or both).
Abstract
Baroclinic instability calculations published by Gall are repeated using the model developed by the authors for use in their own stability studies. Results indicate that some of the differences in the wavelength of maximum linear growth rate found previously may be accounted for by differences in flow profile, but there remains a discrepancy which is a likely consequence of either truncation error in Gall's calculations or a coding error in one or the other model (or both).
Abstract
The growth rate, phase speed, structure and transfer properties of normal modes of the primitive and quasi-geostrophic equations have been determined by applying an initial value technique to global nonlinear atmospheric models. Results are presented for three zonal flows that have the same vertical structure but quite different meridional variations. Use of a variety of vertical and horizontal resolutions gives important indications of truncation error.
Many properties of the unstable modes are much as found in simpler models of baroclinic instability, but spherical geometry has a significant effect on the location of the disturbances, particularly those of low zonal wavenumber, and on eddy momentum fluxes. The latter vary greatly from profile to profile, but mean meridional circulations are such as to give little net variation in the pattern of induced mean zonal surface winds. In fact, the change in vertical shear at the surface is shown to depend in the quasi-geostrophic limit only on the poleward eddy heat flux, which varies little, except in meridional position. Quasi-geostrophic solutions are generally similar to those of the primitive equations, although small differences are often of consistent sign. However, neglect of vertical eddy heat transfer, and to a lesser extent momentum transfer, is a poor approximation.
The present results are in some qualitative agreement with others obtained independently using two-level models, but such models are shown to be subject to severe quantitative error. More generally, vertical truncation error is found to give rise to spurious high-wavenumber growth.
Abstract
The growth rate, phase speed, structure and transfer properties of normal modes of the primitive and quasi-geostrophic equations have been determined by applying an initial value technique to global nonlinear atmospheric models. Results are presented for three zonal flows that have the same vertical structure but quite different meridional variations. Use of a variety of vertical and horizontal resolutions gives important indications of truncation error.
Many properties of the unstable modes are much as found in simpler models of baroclinic instability, but spherical geometry has a significant effect on the location of the disturbances, particularly those of low zonal wavenumber, and on eddy momentum fluxes. The latter vary greatly from profile to profile, but mean meridional circulations are such as to give little net variation in the pattern of induced mean zonal surface winds. In fact, the change in vertical shear at the surface is shown to depend in the quasi-geostrophic limit only on the poleward eddy heat flux, which varies little, except in meridional position. Quasi-geostrophic solutions are generally similar to those of the primitive equations, although small differences are often of consistent sign. However, neglect of vertical eddy heat transfer, and to a lesser extent momentum transfer, is a poor approximation.
The present results are in some qualitative agreement with others obtained independently using two-level models, but such models are shown to be subject to severe quantitative error. More generally, vertical truncation error is found to give rise to spurious high-wavenumber growth.
Abstract
The authors' previous study of baroclinic instability using a primitive equation model with spherical geometry is extended to include more realistic initial distributions of zonal wind and temperature in the upper troposphere and lower stratosphere. Results show little difference in the low-level structure of normal modes, but generally larger upper-level amplitudes for wavelengths close to or longer than that giving maximum linear growth rate. Near the tropopause these disturbances may extend significantly toward the equator, a result shown to be consistent with the forced barotropic response of tropical regions. Their eddy momentum fluxes exhibit some of the variability noted previously, but transfer tends to be predominantly poleward at upper levels. The upper-level heat flux is stronger relative to the momentum flux than is found in general circulation statistics.
Abstract
The authors' previous study of baroclinic instability using a primitive equation model with spherical geometry is extended to include more realistic initial distributions of zonal wind and temperature in the upper troposphere and lower stratosphere. Results show little difference in the low-level structure of normal modes, but generally larger upper-level amplitudes for wavelengths close to or longer than that giving maximum linear growth rate. Near the tropopause these disturbances may extend significantly toward the equator, a result shown to be consistent with the forced barotropic response of tropical regions. Their eddy momentum fluxes exhibit some of the variability noted previously, but transfer tends to be predominantly poleward at upper levels. The upper-level heat flux is stronger relative to the momentum flux than is found in general circulation statistics.
Abstract
It is argued that the essential aspect of atmospheric blocking may be seen in the wave breaking of potential temperature (θ) on a potential vorticity (PV) surface, which may be identified with the tropopause, and the consequent reversal of the usual meridional temperature gradient of θ. A new dynamical blocking index is constructed using a meridional θ difference on a PV surface. Unlike in previous studies, the central blocking latitude about which this difference is constructed is allowed to vary with longitude. At each longitude it is determined by the latitude at which the climatological high-pass transient eddy kinetic energy is a maximum. Based on the blocking index, at each longitude local instantaneous blocking, large-scale blocking, and blocking episodes are defined. For longitudinal sectors, sector blocking and sector blocking episodes are also defined. The 5-yr annual climatologies of the three longitudinally defined blocking event frequencies and the seasonal climatologies of blocking episode frequency are shown. The climatologies all pick out the eastern North Atlantic–Europe and eastern North Pacific–western North America regions. There is evidence that Pacific blocking shifts into the western central Pacific in the summer. Sector blocking episodes of 4 days or more are shown to exhibit different persistence characteristics to shorter events, showing that blocking is not just the long timescale tail end of a distribution. The PV–θ index results for the annual average location of Pacific blocking agree with synoptic studies but disagree with modern quantitative height field–based studies. It is considered that the index used here is to be preferred anyway because of its dynamical basis. However, the longitudinal discrepancy is found to be associated with the use in the height field index studies of a central blocking latitude that is independent of longitude. In particular, the use in the North Pacific of a latitude that is suitable for the eastern North Atlantic leads to spurious categorization of blocking there. Furthermore, the PV–θ index is better able to detect Ω blocking than conventional height field indices.
Abstract
It is argued that the essential aspect of atmospheric blocking may be seen in the wave breaking of potential temperature (θ) on a potential vorticity (PV) surface, which may be identified with the tropopause, and the consequent reversal of the usual meridional temperature gradient of θ. A new dynamical blocking index is constructed using a meridional θ difference on a PV surface. Unlike in previous studies, the central blocking latitude about which this difference is constructed is allowed to vary with longitude. At each longitude it is determined by the latitude at which the climatological high-pass transient eddy kinetic energy is a maximum. Based on the blocking index, at each longitude local instantaneous blocking, large-scale blocking, and blocking episodes are defined. For longitudinal sectors, sector blocking and sector blocking episodes are also defined. The 5-yr annual climatologies of the three longitudinally defined blocking event frequencies and the seasonal climatologies of blocking episode frequency are shown. The climatologies all pick out the eastern North Atlantic–Europe and eastern North Pacific–western North America regions. There is evidence that Pacific blocking shifts into the western central Pacific in the summer. Sector blocking episodes of 4 days or more are shown to exhibit different persistence characteristics to shorter events, showing that blocking is not just the long timescale tail end of a distribution. The PV–θ index results for the annual average location of Pacific blocking agree with synoptic studies but disagree with modern quantitative height field–based studies. It is considered that the index used here is to be preferred anyway because of its dynamical basis. However, the longitudinal discrepancy is found to be associated with the use in the height field index studies of a central blocking latitude that is independent of longitude. In particular, the use in the North Pacific of a latitude that is suitable for the eastern North Atlantic leads to spurious categorization of blocking there. Furthermore, the PV–θ index is better able to detect Ω blocking than conventional height field indices.
Abstract
The summer subtropical circulation in the lower troposphere is characterized by continental monsoon rains and anticyclones over the oceans. In winter, the subtropical circulation is more strongly dominated by the zonally averaged flow and its interactions with orography. Here, the mechanics of the summer and winter lower-tropospheric subtropical circulation are explored through the use of a primitive equation model and comparison with observations.
By prescribing in the model the heatings associated with several of the world's monsoons, it is confirmed that the equatorward portion of each subtropical anticyclone may be viewed as the Kelvin wave response to the monsoon heating over the continent to the west. A poleward-flowing low-level jet into a monsoon (such as the Great Plains jet) is required for Sverdrup vorticity balance. This jet effectively closes off the subtropical anticyclone to the east and also transports moisture into the monsoon region. The low-level jet into North America induced by its monsoon heating is augmented by a remote response to the Asian monsoon heating.
The Rossby wave response to the west of subtropical monsoon heating, interacting with the midlatitude westerlies, produces a region of adiabatic descent. It is demonstrated here that a local “diabatic enhancement” can lead to a strengthening of the descent. Longitudinal mountain chains act to block the westerly flow and also tend to produce descent in this region. Below the descent, Sverdrup vorticity balance implies equatorward flow that closes off the subtropical anticyclone to the west and induces cool upwelling in the ocean through Ekman transport. Feedbacks, involving, for example, sea surface temperatures, may further enhance the descent in these regions. The conclusion is that the Mediterranean-type climates of regions such as California and Chile may be induced remotely by the monsoon to the east.
Hence it can be argued that the subtropical circulation in summer comprises a set of weakly interacting monsoon systems, each involving monsoon rains, a low-level poleward jet, a subtropical anticyclone to the east, and descent and equatorward flow to the west.
In winter, it is demonstrated how the nonlinear interaction between the strong zonal-mean circulation, associated with the winter “Hadley cell,” and the mountains can define many of the large-scale features of the subtropical circulation. The blocking effect of the longitudinal mountain chains is shown to be very important. Subsequent diabatic effects, such as a local diabatic enhancement, would appear to be essential for producing the observed amplitude of these features.
Abstract
The summer subtropical circulation in the lower troposphere is characterized by continental monsoon rains and anticyclones over the oceans. In winter, the subtropical circulation is more strongly dominated by the zonally averaged flow and its interactions with orography. Here, the mechanics of the summer and winter lower-tropospheric subtropical circulation are explored through the use of a primitive equation model and comparison with observations.
By prescribing in the model the heatings associated with several of the world's monsoons, it is confirmed that the equatorward portion of each subtropical anticyclone may be viewed as the Kelvin wave response to the monsoon heating over the continent to the west. A poleward-flowing low-level jet into a monsoon (such as the Great Plains jet) is required for Sverdrup vorticity balance. This jet effectively closes off the subtropical anticyclone to the east and also transports moisture into the monsoon region. The low-level jet into North America induced by its monsoon heating is augmented by a remote response to the Asian monsoon heating.
The Rossby wave response to the west of subtropical monsoon heating, interacting with the midlatitude westerlies, produces a region of adiabatic descent. It is demonstrated here that a local “diabatic enhancement” can lead to a strengthening of the descent. Longitudinal mountain chains act to block the westerly flow and also tend to produce descent in this region. Below the descent, Sverdrup vorticity balance implies equatorward flow that closes off the subtropical anticyclone to the west and induces cool upwelling in the ocean through Ekman transport. Feedbacks, involving, for example, sea surface temperatures, may further enhance the descent in these regions. The conclusion is that the Mediterranean-type climates of regions such as California and Chile may be induced remotely by the monsoon to the east.
Hence it can be argued that the subtropical circulation in summer comprises a set of weakly interacting monsoon systems, each involving monsoon rains, a low-level poleward jet, a subtropical anticyclone to the east, and descent and equatorward flow to the west.
In winter, it is demonstrated how the nonlinear interaction between the strong zonal-mean circulation, associated with the winter “Hadley cell,” and the mountains can define many of the large-scale features of the subtropical circulation. The blocking effect of the longitudinal mountain chains is shown to be very important. Subsequent diabatic effects, such as a local diabatic enhancement, would appear to be essential for producing the observed amplitude of these features.
Abstract
The existence of boundary baroclinic instability (as exemplified by the Eady or Charney problems) and internal baroclinic instability, which requires the potential vorticity gradient to take both signs in the fluid interior, is unified by regarding the boundary temperature gradients in the external problem as equivalent to infinitely thin sheets of nonzero potential vorticity gradient. It is shown that this analogy can be generalized from the quasi-geostrophic to the primitive equation systems. The linear instability problem on the sphere is examined using the primitive equations; the results are consistent with those of simple conceptual models where potential vorticity gradients are concentrated in thin sheets. The normal modes are integrated into the nonlinear regime, and it is shown that the low-level potential vorticity gradients evolve in a similar way to the surface temperature fields in the lifecycles of external modes. Frontal structures are absent, though the enstrophy cascade produces narrow, elongated low-level features around the time of maximum wave activity, Finally, a lifecycle for a boundary unstable flow is compared with that for an initial flow, which is identical except that the surface potential vorticity sheet is thickened to form a finite layer of negative potential vorticity gradient. The evolution of the two cases is remarkably similar except for frontogenesis in the external case.
Abstract
The existence of boundary baroclinic instability (as exemplified by the Eady or Charney problems) and internal baroclinic instability, which requires the potential vorticity gradient to take both signs in the fluid interior, is unified by regarding the boundary temperature gradients in the external problem as equivalent to infinitely thin sheets of nonzero potential vorticity gradient. It is shown that this analogy can be generalized from the quasi-geostrophic to the primitive equation systems. The linear instability problem on the sphere is examined using the primitive equations; the results are consistent with those of simple conceptual models where potential vorticity gradients are concentrated in thin sheets. The normal modes are integrated into the nonlinear regime, and it is shown that the low-level potential vorticity gradients evolve in a similar way to the surface temperature fields in the lifecycles of external modes. Frontal structures are absent, though the enstrophy cascade produces narrow, elongated low-level features around the time of maximum wave activity, Finally, a lifecycle for a boundary unstable flow is compared with that for an initial flow, which is identical except that the surface potential vorticity sheet is thickened to form a finite layer of negative potential vorticity gradient. The evolution of the two cases is remarkably similar except for frontogenesis in the external case.
Abstract
A three-dimensional semi-geostrophic model is used to study the nonlinear development of baroclinic waves on a zonal jet in a model atmosphere with a large change in potential vorticity in the region of the tropopause. The surface frontogenesis proceeds much as in the previous studies in which the tropopause was represented by a lid. However, the upper air development is much more realistic. In particular, there is a locally indirect forcing of the vertical circulation in the region of the upper air front which is easily understood in the present content.
Abstract
A three-dimensional semi-geostrophic model is used to study the nonlinear development of baroclinic waves on a zonal jet in a model atmosphere with a large change in potential vorticity in the region of the tropopause. The surface frontogenesis proceeds much as in the previous studies in which the tropopause was represented by a lid. However, the upper air development is much more realistic. In particular, there is a locally indirect forcing of the vertical circulation in the region of the upper air front which is easily understood in the present content.
