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## Abstract

Terms in the linearized primitive equations for a generally baroclinic atmosphere are evaluated for their significance in maintaining balance for global-scale disturbances. For gravity waves, the linearized advection term v′˙∇ reduces to the vertical component, but for Rossby waves, apparently both components are of primary order. Both wind shear terms are shown to be small for the Rossby case. As a by-product of the scaling developed, the traditional viscous and thermal diffusion terms are reduced to simple forms.

The disturbance energy equation is developed for the general basic state, and the influence that the approximations have on its balance is evaluated.

## Abstract

Terms in the linearized primitive equations for a generally baroclinic atmosphere are evaluated for their significance in maintaining balance for global-scale disturbances. For gravity waves, the linearized advection term v′˙∇ reduces to the vertical component, but for Rossby waves, apparently both components are of primary order. Both wind shear terms are shown to be small for the Rossby case. As a by-product of the scaling developed, the traditional viscous and thermal diffusion terms are reduced to simple forms.

The disturbance energy equation is developed for the general basic state, and the influence that the approximations have on its balance is evaluated.

## Abstract

Monitoring climate variability from space is considered from the standpoint of satellite sampling. Asynoptic sampling leads to well-defined limits in spatial and temporal resolution which are violated by behavior involving sufficiently small scales. Because of aliasing to larger scales, unresolved behavior can influence long-term and spatially averaged behavior important in climate.

From physical processes operating within the climate system, two classes of space-time variability which challenge the information content of asynoptic sampling are identified. Random fluctuations coherent on small space and time scales are characteristic of convective processes in the troposphere and of the dispersion of long-lived constituents such as ozone in the lower stratosphere. Diurnal variations are also an important component of tropospheric convection, as they are of short-lived chemical species such as ozone in the upper stratosphere. Each of these forms of variability can violate the sampling limitations inherent to satellite data from a single orbiting platform.

Implications of undersampling to instantaneous and long-term mean diagnostics are discussed for each of these classes of behavior for orbital and viewing geometries relevant to climate. When the field being monitored has significant variance beyond the Nyquist limits of asynoptic sampling, the complete space-time behavior cannot be recovered faithfully. Diagnostics such as synoptic maps and space-time spectra are prone to contamination from unresolved scales. Aliasing from unresolved random variability cancels in averages over a sufficiently long record, leading to accurate time-mean behavior provided no other forms of unresolved variability are present. A similar cancellation occurs for unresolved diurnal variability if the satellite orbit precesses through local time.

Through careful selection of sampling, long-term mean diagnostics can in principle be retrieved from a single orbiting platform even though the complete behavior may be seriously undersampled. Although such diagnostics represent the primary tool for studying climate, it may be necessary to observe behavior on shorter time scales (e.g., diurnal) to meaningfully interpret these quantities and understand how changes in the climate system occur. To do so will require measurements from multiple orbiting platforms. Sampling strategies and how such measurements can be assimilated so as to recover the full information content of the collective data are suggested.

## Abstract

Monitoring climate variability from space is considered from the standpoint of satellite sampling. Asynoptic sampling leads to well-defined limits in spatial and temporal resolution which are violated by behavior involving sufficiently small scales. Because of aliasing to larger scales, unresolved behavior can influence long-term and spatially averaged behavior important in climate.

From physical processes operating within the climate system, two classes of space-time variability which challenge the information content of asynoptic sampling are identified. Random fluctuations coherent on small space and time scales are characteristic of convective processes in the troposphere and of the dispersion of long-lived constituents such as ozone in the lower stratosphere. Diurnal variations are also an important component of tropospheric convection, as they are of short-lived chemical species such as ozone in the upper stratosphere. Each of these forms of variability can violate the sampling limitations inherent to satellite data from a single orbiting platform.

Implications of undersampling to instantaneous and long-term mean diagnostics are discussed for each of these classes of behavior for orbital and viewing geometries relevant to climate. When the field being monitored has significant variance beyond the Nyquist limits of asynoptic sampling, the complete space-time behavior cannot be recovered faithfully. Diagnostics such as synoptic maps and space-time spectra are prone to contamination from unresolved scales. Aliasing from unresolved random variability cancels in averages over a sufficiently long record, leading to accurate time-mean behavior provided no other forms of unresolved variability are present. A similar cancellation occurs for unresolved diurnal variability if the satellite orbit precesses through local time.

Through careful selection of sampling, long-term mean diagnostics can in principle be retrieved from a single orbiting platform even though the complete behavior may be seriously undersampled. Although such diagnostics represent the primary tool for studying climate, it may be necessary to observe behavior on shorter time scales (e.g., diurnal) to meaningfully interpret these quantities and understand how changes in the climate system occur. To do so will require measurements from multiple orbiting platforms. Sampling strategies and how such measurements can be assimilated so as to recover the full information content of the collective data are suggested.

## Abstract

A 3D model of dynamics and photochemistry is used to investigate interannual changes of stratospheric dynamical and chemical structure through their dependence on tropospheric planetary waves and on the quasi-biennial oscillation (QBO). The integrations reproduce the salient features of the climate sensitivities of temperature and ozone, which have been composited from the observed records of ECMWF and the Total Ozone Mapping Spectrometer (TOMS). Characterized by a strong anomaly of one sign at polar latitudes and a comparatively weak anomaly of opposite sign at subpolar latitudes, each bears the signature of the residual mean circulation. The structure is very similar to that associated with the Arctic Oscillation.

The integrations imply that, jointly, anomalous Eliassen–Palm (EP) flux transmitted from the troposphere by planetary waves and the QBO are the major mechanisms behind interannual changes in the stratosphere. An analogous conclusion follows from the observational record. During early winter, anomalous temperature and ozone are accounted for almost entirely by anomalous EP flux from the troposphere, as they are in the observational record. During late winter, both mechanisms are required to reproduce observed anomalies. Although the QBO forces anomalous structure equatorward of 40°N, the strong anomaly over the Arctic follows principally from anomalous upward EP flux. Reflecting anomalous wave driving of residual mean motion, the change of EP flux leads to anomalous downwelling of ozone-rich air. In concert with isentropic mixing by planetary waves, the anomalous enrichment that ensues at extratropical latitudes sharply modifies total ozone over the Arctic. Integrations distinguished by the omission of heterogeneous processes indicate that chemical destruction accounts for approximately 20% of the anomaly in Arctic ozone between warm and cold winters. Analogous to estimates derived from the observed record of the Solar Backscatter Ultraviolet, version 8 (SBUV-V8) instrument, the remaining approximately 80% follows from anomalous transport.

The climate sensitivities of temperature and ozone describe random changes between years, introduced by anomalous EP flux and the QBO. Those interannual changes evolve with a particular seasonality. Like their structure, the seasonal dependence of anomalous temperature and ozone bears the signature of the residual mean circulation. Systematic changes in the observed record, which comprise stratospheric trends, have similar structure and seasonality.

## Abstract

A 3D model of dynamics and photochemistry is used to investigate interannual changes of stratospheric dynamical and chemical structure through their dependence on tropospheric planetary waves and on the quasi-biennial oscillation (QBO). The integrations reproduce the salient features of the climate sensitivities of temperature and ozone, which have been composited from the observed records of ECMWF and the Total Ozone Mapping Spectrometer (TOMS). Characterized by a strong anomaly of one sign at polar latitudes and a comparatively weak anomaly of opposite sign at subpolar latitudes, each bears the signature of the residual mean circulation. The structure is very similar to that associated with the Arctic Oscillation.

The integrations imply that, jointly, anomalous Eliassen–Palm (EP) flux transmitted from the troposphere by planetary waves and the QBO are the major mechanisms behind interannual changes in the stratosphere. An analogous conclusion follows from the observational record. During early winter, anomalous temperature and ozone are accounted for almost entirely by anomalous EP flux from the troposphere, as they are in the observational record. During late winter, both mechanisms are required to reproduce observed anomalies. Although the QBO forces anomalous structure equatorward of 40°N, the strong anomaly over the Arctic follows principally from anomalous upward EP flux. Reflecting anomalous wave driving of residual mean motion, the change of EP flux leads to anomalous downwelling of ozone-rich air. In concert with isentropic mixing by planetary waves, the anomalous enrichment that ensues at extratropical latitudes sharply modifies total ozone over the Arctic. Integrations distinguished by the omission of heterogeneous processes indicate that chemical destruction accounts for approximately 20% of the anomaly in Arctic ozone between warm and cold winters. Analogous to estimates derived from the observed record of the Solar Backscatter Ultraviolet, version 8 (SBUV-V8) instrument, the remaining approximately 80% follows from anomalous transport.

The climate sensitivities of temperature and ozone describe random changes between years, introduced by anomalous EP flux and the QBO. Those interannual changes evolve with a particular seasonality. Like their structure, the seasonal dependence of anomalous temperature and ozone bears the signature of the residual mean circulation. Systematic changes in the observed record, which comprise stratospheric trends, have similar structure and seasonality.

## Abstract

The influence of large-scale transience on horizontal air motions and tracer distributions in the stratosphere is explored in equivalent barotropic calculations. Planetary waves are excited by steady and unsteady components of mechanical forcing that are assigned variances typical of variability in the stratosphere. Two classes of transience are considered. A monochromatic traveling wave, representative of discrete components such as the 5- and 16-day waves, is imposed as unsteady mechanical forcing. The system is also forced by a second-order stochastic process representative of broadband variability. The response to each of these forms of unsteady forcing is investigated in terms of the characteristic time scale of the transience.

For monochromatic transience, eddy transport is concentrated inside the critical region of the traveling wave, for example, where perturbation velocities become comparable to the Doppler-shifted flow. There, eddy displacements are large enough for nonconservative behavior and net transport to occur, which leave a permanent influence on the circulation and tracer distributions. Eddy transport is greatest for low-frequency disturbances because the critical region of the traveling wave then overlaps that of the stationary wave. During constructive interference, eddy displacements of the traveling wave reinforce those of the stationary wave. The nonlinear interaction that takes place between the two components leads to an expanded critical region and more extensive transport. In contrast, high-frequency traveling waves have large Doppler-shifted flows everywhere. Air motions associated with such disturbances are nearly reversible, leaving only a small permanent influence on the circulation and tracer distributions.

For stochastic transience, all frequencies are present. The critical region and eddy transport are then smeared across the globe. As a result, eddy transport is weaker locally than that concentrated inside the critical region of a monochromatic traveling wave with the same variance. Only those spectral components slow enough to be Doppler shifted to small intrinsic phase speeds exert a lasting influence on the circulation. Consequently, transience distributed over a wide range of frequency (e.g., spectrally “white”) produces less overall transport than transience concentrated at low frequencies (e.g., spectrally “red”). Stochastic forcing also excites westward-propagating transients that radiate into the summer hemisphere and disperse globally into planetary normal modes. Favored in the response to broadband forcing, those discrete components lead to behavior similar to that of traveling waves excited by monochromatic forcing. By introducing nonconservative behavior in regions where they reinforce large displacements of the stationary wave and where they themselves are Doppler shifted to small intrinsic phase speeds, these unsteady components can contribute to the momentum budgets of both the wintertime and the summertime circulations.

## Abstract

The influence of large-scale transience on horizontal air motions and tracer distributions in the stratosphere is explored in equivalent barotropic calculations. Planetary waves are excited by steady and unsteady components of mechanical forcing that are assigned variances typical of variability in the stratosphere. Two classes of transience are considered. A monochromatic traveling wave, representative of discrete components such as the 5- and 16-day waves, is imposed as unsteady mechanical forcing. The system is also forced by a second-order stochastic process representative of broadband variability. The response to each of these forms of unsteady forcing is investigated in terms of the characteristic time scale of the transience.

For monochromatic transience, eddy transport is concentrated inside the critical region of the traveling wave, for example, where perturbation velocities become comparable to the Doppler-shifted flow. There, eddy displacements are large enough for nonconservative behavior and net transport to occur, which leave a permanent influence on the circulation and tracer distributions. Eddy transport is greatest for low-frequency disturbances because the critical region of the traveling wave then overlaps that of the stationary wave. During constructive interference, eddy displacements of the traveling wave reinforce those of the stationary wave. The nonlinear interaction that takes place between the two components leads to an expanded critical region and more extensive transport. In contrast, high-frequency traveling waves have large Doppler-shifted flows everywhere. Air motions associated with such disturbances are nearly reversible, leaving only a small permanent influence on the circulation and tracer distributions.

For stochastic transience, all frequencies are present. The critical region and eddy transport are then smeared across the globe. As a result, eddy transport is weaker locally than that concentrated inside the critical region of a monochromatic traveling wave with the same variance. Only those spectral components slow enough to be Doppler shifted to small intrinsic phase speeds exert a lasting influence on the circulation. Consequently, transience distributed over a wide range of frequency (e.g., spectrally “white”) produces less overall transport than transience concentrated at low frequencies (e.g., spectrally “red”). Stochastic forcing also excites westward-propagating transients that radiate into the summer hemisphere and disperse globally into planetary normal modes. Favored in the response to broadband forcing, those discrete components lead to behavior similar to that of traveling waves excited by monochromatic forcing. By introducing nonconservative behavior in regions where they reinforce large displacements of the stationary wave and where they themselves are Doppler shifted to small intrinsic phase speeds, these unsteady components can contribute to the momentum budgets of both the wintertime and the summertime circulations.

## Abstract

The existence of planetary normal modes in the presence of realistic mean fields is examined. For sufficiently large wavenumber *m*, or meridional index *n*, the response of the Rossby modes is diffused beyond identification. This is primarily a result of the Doppler shifting of mean winds and supersedes the increasing role of dissipation.

Several initial modes for the first few wavenumbers should be both realizable and identifiable in typical conditions. “At least” the first three modes of wavenumber 1, the first two of wavenumber 2, and the first of wavenumber 3 should occur with periods isolated to within 12.5% of median values. The mode structures for the first four modes of wavenumbers 1, 2 and 3 are insensitive to the mean fields in the lowest two scale heights. In addition, the response of each of these is readily discernable in both equinox and solstice conditions.

The modes' horizontal character is notably robust. Although the solutions typically exhibit regions where they are affected by the mean fields, the domain of influence is local. Vertical growth rates tend to be magnified in regions where the winds are weak westerly relative to the wave or the temperature gradient is equatorward, while amplitudes evanesce in regions of strong westerlies or poleward temperature gradient. The former give rise to enhanced amplitudes in the equinox stratosphere and the summer mesosphere.

Results calculated here for the first symmetric wavenumber 1 mode are in close agreement with those found by Geisler and Dickinson (1976). Moreover, the estimate for the possible spread of variance compares favorably with the 4–6 day range existing in the observational evidence. Calculations for the second symmetric wavenumber 1 mode support Madden's (1978) identification of the 16-day wavenumber 1 disturbance with the (*m*, *n* − *m*)=(1, 3) mode. In the presence of uniform surface forcing, the peak response is very near 16 days. More importantly, the estimate of possible spread in variance is compatible with the observed 1–3 week range for the disturbance. Although its structure is largely unaffected in the first few scale heights, the mode attains large amplitudes in the winter stratosphere of the solstice configuration. Finally, a number of observed features of the 2-day wave in the upper atmosphere suggest its identification with the third Rossby-gravity mode, which corresponds well in both temporal and spatial character.

## Abstract

The existence of planetary normal modes in the presence of realistic mean fields is examined. For sufficiently large wavenumber *m*, or meridional index *n*, the response of the Rossby modes is diffused beyond identification. This is primarily a result of the Doppler shifting of mean winds and supersedes the increasing role of dissipation.

Several initial modes for the first few wavenumbers should be both realizable and identifiable in typical conditions. “At least” the first three modes of wavenumber 1, the first two of wavenumber 2, and the first of wavenumber 3 should occur with periods isolated to within 12.5% of median values. The mode structures for the first four modes of wavenumbers 1, 2 and 3 are insensitive to the mean fields in the lowest two scale heights. In addition, the response of each of these is readily discernable in both equinox and solstice conditions.

The modes' horizontal character is notably robust. Although the solutions typically exhibit regions where they are affected by the mean fields, the domain of influence is local. Vertical growth rates tend to be magnified in regions where the winds are weak westerly relative to the wave or the temperature gradient is equatorward, while amplitudes evanesce in regions of strong westerlies or poleward temperature gradient. The former give rise to enhanced amplitudes in the equinox stratosphere and the summer mesosphere.

Results calculated here for the first symmetric wavenumber 1 mode are in close agreement with those found by Geisler and Dickinson (1976). Moreover, the estimate for the possible spread of variance compares favorably with the 4–6 day range existing in the observational evidence. Calculations for the second symmetric wavenumber 1 mode support Madden's (1978) identification of the 16-day wavenumber 1 disturbance with the (*m*, *n* − *m*)=(1, 3) mode. In the presence of uniform surface forcing, the peak response is very near 16 days. More importantly, the estimate of possible spread in variance is compatible with the observed 1–3 week range for the disturbance. Although its structure is largely unaffected in the first few scale heights, the mode attains large amplitudes in the winter stratosphere of the solstice configuration. Finally, a number of observed features of the 2-day wave in the upper atmosphere suggest its identification with the third Rossby-gravity mode, which corresponds well in both temporal and spatial character.

## Abstract

The information content of asynoptic satellite data is evaluated for nadir sonde and limb scan observations. Orbital sampling patterns are shown to uniquely determine the space-time spectrum, within well-defined sampling limitations. The latter turn out to be a hybrid of wavenumber and frequency in the same manner that the observations are a mixture of space and time. Space-time spectra thus computed are correct throughout the allowed region of wavenumber and frequency. Complexities such as orbital tilt and day-to-day drift of the nodes, are completely accounted for.

The allowed region of spectra, which defines the information content, is a rectangle in Fourier space, rotated relative to the wavenumber, frequency axes. This rotation is a consequence of the lack of simultaneity in the observations. For “single-node” data, the aliasing limitations correspond approximately to a maximum wavenumber of half the orbital frequency (orbits per day) and frequency extrema of ±0.5 cpd. Definition of the sampling restrictions for “combined-node” (ascending + descending) data is complicated by the introduction of additional aliasing. The latter, which arises from irregular sampling, ultimately from orbital tilt, is serious at middle and high latitudes, where ascending and descending nodes converge. This additional contamination is inherent to combined asynoptic data. It results from the unequal spacing between ascending and descending nodes. Consequently, spectra calculated via the transform, or other form of projection, must be restricted to frequencies less than 0.5 cpd, thus not fully utilizing the combined observations.

The additional contamination can be completely eliminated by replacing the transform along the coordinate of irregular sampling, with explicit evaluation of the Fourier components. Then the region of allowed spectra can be extended to frequencies of ±1.0 cpd, i.e., a doubling in resolution over single-node data. The allowed region is shown to be analogous to that of “twice-daily,” synoptic sampling at equispaced points, equal in number to approximately the orbital frequency. The resulting formulas constitute the Asynoptic Sampling Theorem: uniquely relating a combined asynoptic data set to its space-time spectrum.

## Abstract

The information content of asynoptic satellite data is evaluated for nadir sonde and limb scan observations. Orbital sampling patterns are shown to uniquely determine the space-time spectrum, within well-defined sampling limitations. The latter turn out to be a hybrid of wavenumber and frequency in the same manner that the observations are a mixture of space and time. Space-time spectra thus computed are correct throughout the allowed region of wavenumber and frequency. Complexities such as orbital tilt and day-to-day drift of the nodes, are completely accounted for.

The allowed region of spectra, which defines the information content, is a rectangle in Fourier space, rotated relative to the wavenumber, frequency axes. This rotation is a consequence of the lack of simultaneity in the observations. For “single-node” data, the aliasing limitations correspond approximately to a maximum wavenumber of half the orbital frequency (orbits per day) and frequency extrema of ±0.5 cpd. Definition of the sampling restrictions for “combined-node” (ascending + descending) data is complicated by the introduction of additional aliasing. The latter, which arises from irregular sampling, ultimately from orbital tilt, is serious at middle and high latitudes, where ascending and descending nodes converge. This additional contamination is inherent to combined asynoptic data. It results from the unequal spacing between ascending and descending nodes. Consequently, spectra calculated via the transform, or other form of projection, must be restricted to frequencies less than 0.5 cpd, thus not fully utilizing the combined observations.

The additional contamination can be completely eliminated by replacing the transform along the coordinate of irregular sampling, with explicit evaluation of the Fourier components. Then the region of allowed spectra can be extended to frequencies of ±1.0 cpd, i.e., a doubling in resolution over single-node data. The allowed region is shown to be analogous to that of “twice-daily,” synoptic sampling at equispaced points, equal in number to approximately the orbital frequency. The resulting formulas constitute the Asynoptic Sampling Theorem: uniquely relating a combined asynoptic data set to its space-time spectrum.

## Abstract

Two classes of tropical cloud variability: (i) random small-scale fluctuations and (ii) diurnal variations, are investigated with regard to deriving fields of emitted radiation from wide-field-of-view (WFOV) measurements of outgoing radiance made aboard polar orbiting satellites. Irregular cloud variability is represented in terms of a stochastic space-time process defined by prescribed spatial and temporal correlation scales and confined to an envelope typical of tropical convective centers. Diurnal cloud variability is prescribed in terms of a propagating solar waveform which likewise is confined to a horizontal envelope. For both classes of convective behavior, the evolving radiation field is sampled asynoptically, deconvolved, and compared with the true variability. A variety of diagnostics is examined, including space-time power spectra, instantaneous synoptic behavior, and time-mean fields. Sensitivity to spatial and temporal scales of the convective pattern, (correlation scales in the case of random variability) is evaluated for both classes of behavior.

For realistic convective scales, the retrieved behavior is aliased by unresolved variability. Of the two classes of convective behavior, diurnal variations pose the most serious challenge to the sampling, because they introduce variance well removed from the Nyquist limits of asynoptic observations. Moreover, while unresolved behavior may be eliminated by time averaging in the case of random variability, diurnal variations alias to steady components whose influence remains even in time-mean fields. These aliases would be expected to seriously contaminate monthly- and seasonal-mean behavior over tropical landmasses, where diurnal viability is large.

Contemporaneous WFOV measurements from several satellites orbiting the globe (e.g., ERBE) may hold the solution to the problem. The expanded information content, represented by the combined data, should capture most if not all of the large-scale variability unresolved by single satellite sampling. An added and unique advantage of WFOV observations is that mesoscale convective complexes, which are predominant in tropical convection but which may only be resolved with a geostationary platform, are automatically removed–without aliasing, leaving behind the large-scale filtered field which is resolvable and of primary interest for many applications. Extending the resolution of asynoptic measurements with multiple satellite data will require that sampling asymmetries, inherent to the combined data ensemble, be *explicitly* accounted for. With the majority of cloud brightness variability captured by the combined sampling, this would place within grasp faithful recovery of, not only the large-scale time-mean field, but the complete synoptic structure and evolution as well.

## Abstract

Two classes of tropical cloud variability: (i) random small-scale fluctuations and (ii) diurnal variations, are investigated with regard to deriving fields of emitted radiation from wide-field-of-view (WFOV) measurements of outgoing radiance made aboard polar orbiting satellites. Irregular cloud variability is represented in terms of a stochastic space-time process defined by prescribed spatial and temporal correlation scales and confined to an envelope typical of tropical convective centers. Diurnal cloud variability is prescribed in terms of a propagating solar waveform which likewise is confined to a horizontal envelope. For both classes of convective behavior, the evolving radiation field is sampled asynoptically, deconvolved, and compared with the true variability. A variety of diagnostics is examined, including space-time power spectra, instantaneous synoptic behavior, and time-mean fields. Sensitivity to spatial and temporal scales of the convective pattern, (correlation scales in the case of random variability) is evaluated for both classes of behavior.

For realistic convective scales, the retrieved behavior is aliased by unresolved variability. Of the two classes of convective behavior, diurnal variations pose the most serious challenge to the sampling, because they introduce variance well removed from the Nyquist limits of asynoptic observations. Moreover, while unresolved behavior may be eliminated by time averaging in the case of random variability, diurnal variations alias to steady components whose influence remains even in time-mean fields. These aliases would be expected to seriously contaminate monthly- and seasonal-mean behavior over tropical landmasses, where diurnal viability is large.

Contemporaneous WFOV measurements from several satellites orbiting the globe (e.g., ERBE) may hold the solution to the problem. The expanded information content, represented by the combined data, should capture most if not all of the large-scale variability unresolved by single satellite sampling. An added and unique advantage of WFOV observations is that mesoscale convective complexes, which are predominant in tropical convection but which may only be resolved with a geostationary platform, are automatically removed–without aliasing, leaving behind the large-scale filtered field which is resolvable and of primary interest for many applications. Extending the resolution of asynoptic measurements with multiple satellite data will require that sampling asymmetries, inherent to the combined data ensemble, be *explicitly* accounted for. With the majority of cloud brightness variability captured by the combined sampling, this would place within grasp faithful recovery of, not only the large-scale time-mean field, but the complete synoptic structure and evolution as well.

## Abstract

The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index *n*. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing *n*, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below.

Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater dissipation.

In view of the absence of steady forcing mechanisms for these modes, several hypothetical transient situations are examined. The implication of finite relaxation periods to intermittent reinforcement is discussed, and the relative importance of local dissipation versus vertical leakage is considered. Estimates of damping times here together with recent observations of the 5-day wave, suggest that should slower modes, be excited, they would exist only in a transient sense.

The existence of modes ducted horizontally by realistic variations in the mean fields is also considered. If the trapping occurs sufficiently high (greater than the first few scale heights). the, wave duct cannot be excited by forcing near the surface, since the energy flux reaching these levels is minimal. Wave ducting by vertical variations in temperature could be found, but the response associated with such trapping was small and dwarfed by that of the Lamb structure at all heights. The vertical *e* folding distance for the energy flux is on the order of a few scale heights, over a broad range of disturbance parameters, for vertically propagating rotational modes. Such behavior. suggests that efficiently ducted rotational modes in the atmosphere are unlikely, leaving the Lamb structure as the only plausible rotational normal feature.

## Abstract

The effect of realistic dissipation on the rotational normal modes of a barotropic atmosphere is investigated. Vertical growth of amplitude of the Lamb(10km equivalent depth)modes is found to diminish with increasing meridional index *n*. The fastest traveling modes are most sensitive to radiative-photo-chemical damping above 4 scale heights. However, with increasing *n*, thermal and viscous diffusion dissipate more of the energy below this level. The energy flux is virtually attenuated by 8 scale heights. Thus the particular details above this level should have little bearing on the nature of the modes below.

Damping time scales (relaxation periods) are estimated for several modes. These are smallest for wavenumber 1, roughly 10 wave periods, and increase with zonal wavenumber. The role of dissipation in determining these relaxation periods is more than just the local damping of energy. It significantly enhances the “vertical leakage” and thus allows energy to flow more readily to levels of greater dissipation.

In view of the absence of steady forcing mechanisms for these modes, several hypothetical transient situations are examined. The implication of finite relaxation periods to intermittent reinforcement is discussed, and the relative importance of local dissipation versus vertical leakage is considered. Estimates of damping times here together with recent observations of the 5-day wave, suggest that should slower modes, be excited, they would exist only in a transient sense.

The existence of modes ducted horizontally by realistic variations in the mean fields is also considered. If the trapping occurs sufficiently high (greater than the first few scale heights). the, wave duct cannot be excited by forcing near the surface, since the energy flux reaching these levels is minimal. Wave ducting by vertical variations in temperature could be found, but the response associated with such trapping was small and dwarfed by that of the Lamb structure at all heights. The vertical *e* folding distance for the energy flux is on the order of a few scale heights, over a broad range of disturbance parameters, for vertically propagating rotational modes. Such behavior. suggests that efficiently ducted rotational modes in the atmosphere are unlikely, leaving the Lamb structure as the only plausible rotational normal feature.

## Abstract

A detailed analysis is made of the spatial and temporal information content of wide-field-of-view (WFOV) measurements of outgoing radiation. Specifically, the spatial resolution of WFOV measurements, commensurate with sampling considerations, is determined. It is shown that asynoptic sampling introduces a more stringent limitation on the resolvable scales than that posed by the stability of the deconvolution procedure used to derive enhanced resolution maps of emitted radiation. In particular, the resolvable zonal wavenumber cannot be defined independently of the temporal behavior. It is demonstrated that the scales which may be unambiguously determined follow from characteristics of the asynoptic sampling, analogous to similar considerations which apply to narrow-field-of-view measurements. Orbital characteristics typical of the Nimbus series lead to zonal resolution out to approximately wavenumber 6.

## Abstract

A detailed analysis is made of the spatial and temporal information content of wide-field-of-view (WFOV) measurements of outgoing radiation. Specifically, the spatial resolution of WFOV measurements, commensurate with sampling considerations, is determined. It is shown that asynoptic sampling introduces a more stringent limitation on the resolvable scales than that posed by the stability of the deconvolution procedure used to derive enhanced resolution maps of emitted radiation. In particular, the resolvable zonal wavenumber cannot be defined independently of the temporal behavior. It is demonstrated that the scales which may be unambiguously determined follow from characteristics of the asynoptic sampling, analogous to similar considerations which apply to narrow-field-of-view measurements. Orbital characteristics typical of the Nimbus series lead to zonal resolution out to approximately wavenumber 6.

## Abstract

The problem of determining the long-period normal modes of a barotropic atmosphere with realistic temperature, distribution and in uniform motion is examined over the entire range of equivalent depth. It is demonstrated that there are only two solutions which satisfy a radiation/finite energy condition and approximately satisfy the homogeneous surface boundary condition. Outside of a particular interval of equivalent depth, it is shown that there exist no solutions. The problem is solved numerically over the restricted interval where two sharp dips in the surface error are found.

The first of these corresponds to a 9.6 km equivalent depth and a Lamb structure. This mode, which is the counterpart of the thin film solutions on a sphere, is due to the hydrostatic nature of the basic state and exists despite the temperature variation. The second dip, corresponding to a 5.8 km equivalent depth here, is a result of buoyancy ducting and is a consequence of the temperature variation. The energy density of this structure has maxima at the surface and at a level appropriate to the stratopause. Because of its more fundamental nature, the Lamb mode satisfies the homogeneous problem to a greater degree and has the greatest likelihood of being realized in the atmosphere. The second structure indicates the potential for wave ducting in the stratosphere and mesosphere. Because of its dependence on the particular nature of the temperature profile, however, its realization in the atmosphere would be more variable.

Local energy residence times are calculated for each mode. The Lamb mode has its greatest value near the surface where the dissipationless estimate exceeds several hundred wave periods in a layer appropriate to the troposphere. The second structure resides longest in a layer appropriate to the stratosphere and mesosphere where energy may remain on the order of 10 periods in the absence of dissipation.

## Abstract

The problem of determining the long-period normal modes of a barotropic atmosphere with realistic temperature, distribution and in uniform motion is examined over the entire range of equivalent depth. It is demonstrated that there are only two solutions which satisfy a radiation/finite energy condition and approximately satisfy the homogeneous surface boundary condition. Outside of a particular interval of equivalent depth, it is shown that there exist no solutions. The problem is solved numerically over the restricted interval where two sharp dips in the surface error are found.

The first of these corresponds to a 9.6 km equivalent depth and a Lamb structure. This mode, which is the counterpart of the thin film solutions on a sphere, is due to the hydrostatic nature of the basic state and exists despite the temperature variation. The second dip, corresponding to a 5.8 km equivalent depth here, is a result of buoyancy ducting and is a consequence of the temperature variation. The energy density of this structure has maxima at the surface and at a level appropriate to the stratopause. Because of its more fundamental nature, the Lamb mode satisfies the homogeneous problem to a greater degree and has the greatest likelihood of being realized in the atmosphere. The second structure indicates the potential for wave ducting in the stratosphere and mesosphere. Because of its dependence on the particular nature of the temperature profile, however, its realization in the atmosphere would be more variable.

Local energy residence times are calculated for each mode. The Lamb mode has its greatest value near the surface where the dissipationless estimate exceeds several hundred wave periods in a layer appropriate to the troposphere. The second structure resides longest in a layer appropriate to the stratosphere and mesosphere where energy may remain on the order of 10 periods in the absence of dissipation.