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Murry L. Salby

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.

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Murry L. Salby

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.

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Murry Salby and Patrick Callaghan

Abstract

NCEP reanalyses are used to isolate systematic variations in the stratosphere that operated coherently over the last four decades with the 11-yr variation of UV irradiance. Only a small systematic variation is visible at low frequency, which would reflect a simple linear response that drifts with solar flux, F s. However, a systematic variation manifests itself prominently at high frequency, which involves changes between neighboring years. Corresponding to interannual variability, the systematic variation at high frequency reflects a more complex, nonlinear response to the 11-yr variation of UV irradiance. It is analogous to a similar variation found earlier in the quasi-biennial oscillation (QBO) of equatorial wind, u EQ.

Interannual variability undergoes a frequency modulation that systematically alters its phase during winter, when planetary waves couple the polar and equatorial stratosphere. The polar-night vortex is then sensitive to equatorial wind, which itself varies systematically with F s. Monte Carlo simulations indicate that the systematic variation of wintertime phase is highly significant.

The systematic variation appears prominently in the wintertime tendency of temperature, which is coupled directly to the residual mean circulation. In fact, the anomalous wintertime tendency operating coherently with F s has the same basic structure as that operating coherently with anomalous forcing of the residual circulation. Each reflects anomalous downwelling over the Arctic that is compensated at lower latitude by anomalous upwelling. The resemblance of these anomalous structures suggests that the systematic variation at high frequency enters through changes of the residual circulation.

Accompanying the variation of zonal-mean structure is a systematic amplification and decay of wavenumber 1 at high latitude. It represents a poleward advance and retreat of the critical region, or surf zone, where planetary waves experience strong absorption that forces residual motion. This variation of wave structure, along with the anomalous residual motion it forces, parallels the systematic variation of equatorial wind. Wintertime-mean u EQ suggests a reversal of anomalous downwelling between solar min and solar max, one broadly consistent with the observed reversal of anomalous temperature.

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Murry L. Salby

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.

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Murry L. Salby

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.

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Murry Salby and Fabrizio Sassi

Abstract

Climate properties regulated by convection, such as water vapor, cloud cover, and related distributions, are undersampled in asynoptic data from an individual orbiting platform, which must therefore be restricted to time-mean distributions. A procedure is developed to identify small-scale undersampled variance in asynoptic data and reject it, leaving a more accurate representation of large-scale variance that describes the organization of climate properties. The procedure is validated against high-resolution distributions that have been constructed from six satellites simultaneously observing the earth. Observing the high-resolution distributions asynoptically is shown to result in sampling error at large scales that is as great as the large-scale signal present, limiting the usefulness of the raw asynoptic data to time-mean distributions. However, processing the asynoptic data to reject undersampled incoherent variability reduces the error variance to 10% or less, yielding a fairly accurate representation of large-scale coherent variability, which then can be mapped synoptically on periods as short as 2.0 days. Made possible then are studies of how cloud, water vapor, and related distributions are organized by unsteady elements of the general circulation, which cannot be studied in the raw asynoptic data.

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Murry L. Salby

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.

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Murry L. Salby

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.

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Murry L. Salby

Abstract

Predominant wavenumber-5 patterns frequent the temperature fields of the lower stratosphere of the Southern Hemisphere during the summer months of FGGE. These pentagonal features, of broad latitudinal extent, appear to remain quasi-stationary or propagate eastward with periods on the order or 10 days.

Ensemble statistics over the summer season confirm the presence of large-amplitude wavenumber-5 anomalies in the geopotential fields. Magnified height amplitudes appear in the zonal spectra at wave 5, near the tropospheric jet core: 50°S and 300 mb. The enhanced temperature anomalies in the lower stratosphere arise not only from the magnified geopotential amplitude of wavenumber 5, but also from its sharp evanescence above the jet. Time series analysis reveals that the peak in rms amplitude results primarily from the fluctuating contribution.

The transient component of wavenumber 5 shows a regular eastward phase progression. Geopotential power spectra exhibit a pronounced peak, corresponding to eastward propagation with a period of approximately 11 days and half-power points at 8 and 15 days. Hence, the disturbances appear concentrated in both wavenumber and frequency. A nearly barotropic phase structure is characteristic of the bandpassed wave field over most of the amplified region, becoming more propagating near the extremities of the disturbance, where the amplitude is weak. Such behavior is suggestive of a partially trapped, or leaky normal feature, probably excited by baroclinic energy conversion. The eastward phase progression and height structure maximizing in the jet are not inconsistent with features of a baroclinically unstable mode. However, the variance peak at relatively low wavenumber, and perhaps more importantly, its discrete character in both space and time, are inconsistent with conventional views of baroclinic instability. Phase structures suggest that the refractive character of the basic flow and perhaps the temperature gradient at the Antarctic escarpment may be involved in the regularity of the disturbance.

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Murry L. Salby

Abstract

A one to one correspondence between alias-free asynoptic data and twice-daily synoptic maps is established in the Synoptic Retrieval Theorem. The uniqueness follows from an extension of the Sampling Theorem.

A Fast Fourier Transform Scheme is defined for retrieving the unique sequence of synoptic maps from the asynoptic observations. The procedure involves the construction of space-time spectra from “irregular,” combined asynoptic data. This is accomplished by application of the asynoptic form of the space-time transform. The “regular” sequence of synoptic maps is then recovered by application of the synoptic form of the inverse space-time transform. Twice-daily, synoptic sequences retrieved in this fashion, contain exactly the correct spectral contribution resolvable in both types of data. The technique conserves information and fully utilizes the information content of combined, asynoptic observations. Furthermore, it is directly amenable to parallel processing of data over large ensembles of latitudes and pressure levels. Temporal evolution is retrieved equally well for both statistically stationary and nonstationary processes.

Intermediate products of the synoptic inversion are global spectra. Their availability during the procedure allows the removal of latitudinally incoherent noise by low-pass filtering. It also makes possible the expansion of observed fields, or equivalently their wavenumber-frequency components, in arbitrary sets of spherical functions. In particular, the projection of remotely derived geopotential components onto Hough harmonics, facilitates the construction of “global” wind fields, thereby circumventing the equatorial problem characteristic of geostrophic treatments.

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