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Alfonso Sutera

Abstract

In this note we study a simple truncated spectral model of a fluid in a pure convective motion due to Lorenz (1963). We find that where the equations are perturbed by a stochastic Wiener process (white noise), the system leaves the attraction domain of stable steady state after a time τ+.

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Barry Saltzman and Alfonso Sutera

Abstract

A simplified version of a previously described dynamical model governing global ice mass, atmospheric carbon dioxide, and mean ocean temperature (that may also be a proxy for some other CO2–controlling oceanic variable, e.g., nutrient supply) is shown to possess solutions, in a realistic parameter range, that can replicate the main features of the climatic variations implied by the full, two million years, Quarternary δ18O record. These variations include a major “transition” between a low-ice (δ18O, low variance mode before roughly 900 kyr BP to a high-ice (near 100 kyr period) variance mode after that time to the present. The model contains only three free parameters in this simplified form. No external earth-orbital forcing is prescribed; i.e., the model represents only internal dynamics. From the previous studies it seems clear that additional variance representing such features as the “rapid” deglaciation and the phase of the major Quaternary oscillation can be largely explained with no more than four additional parameters representing an internal asymmetry and the external periodic forcing. The present results, therefore, constitute a first-order account for the existence of the “ice age” fluctuations over the last two million years, including the concomitant variations of atmospheric CO2. The variations of mean ocean temperature (or a related VO2–controlling proxy variable) are also deduced and represent a side prediction of the model.

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Rodrigo Caballero and Alfonso Sutera

Abstract

The statistical equilibration of baroclinic waves in a two-level quasigeostrophic model subject to forcing and dissipation is studied. The model employed may be formulated in either spherical or Cartesian geometry and is restricted to a midlatitude channel. Parameters are chosen so that only up to three waves can become supercritical (one planetary- and two synoptic-scale waves). It is found that both geometries exhibit essentially two equilibration regimes as the forcing temperature gradient varies. At low forcing, the planetary-scale wave is not excited while the two synoptic-scale waves equilibrate with steady finite amplitude. In this regime, the equilibrated temperature gradient is sensitive to forcing; the authors argue that this is due to the barotropic governor effect. At higher forcing, the planetary wave becomes active and the solution is aperiodic. In this regime, the planetary wave acts to reduce the barotropic shear spun up by the synoptic waves, thereby limiting the role of the barotropic governor; the equilibrated temperature gradient then becomes much less sensitive to forcing. The Cartesian and spherical cases differ both in the structure of the equilibrated state and in the strength of the barotropic governor (which is greater on the sphere). These differences are related to the geometric curvature terms and not to the meridional variation of β.

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Barry Saltzman and Alfonso Sutera

Abstract

Because of the small net rates of energy flow involved in very long-term changes in ice mass (10−1 W m−2) it will be impossible to proceed in a purely deductive manner to develop a theory for these changes. An inductive approach will be necessary-perhaps beg formulated in terms of multi-component stochastic-dynamical systems of equations governing the variables and feedbacks thought to be relevant from qualitative physical reasoning (e.g., “conceptual models”). The output of such models should be required to conform as closely as possible to all lines of observational evidence on climatic change, have a predictive quality in the search for new observational evidence, and satisfy the general conservation laws and all the results of physical measurement of the fast response (high energy flux) processes that generally lead to diagnostic relationships.

A prototype of such an inductive model is described. This model is formulated as a nonlinear dynamical system governing three components: continental ice mass marine ice mass, and bulk ocean temperature. The solution is shown to have several properties in common with geological evidence for the variations of these quantities.

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Anthony R. Hansen and Alfonso Sutera

Abstract

The transient eddy height variance in midlatitudes during Southern Hemisphere (SH) winter achieves its largest value at zonal wavenumber 3. The presence of two highly statistically significant modes in the probability density distribution of the zonal wavenumber 3 amplitude allows one to conclude that this variance is the result of the circulation switching between two statistical flow regimes. One regime is characterized by a predominantly wavenumber 1 pattern and the other by an amplified wavenumber 3 pattern. The probability density distributions of the duration of these two regimes can be roughly approximated as exponential functions with e-folding times of 6 to 12 days. Thus, on the intraseasonal time scale during SH winter, the time mean flow is not the most probable state of the circulation. In contrast, during SH summer no bimodality occurs and the wavenumber 3 probability density distribution is strongly skewed toward the winter low amplitude mode.

Simple energetics considerations suggest that in SH winter wave-wave interaction between intermediate-scale eddies (wavenumbers 5 to 7) and wavenumber 3 is a significant energy source to maintain the amplified wave pattern, while wave-mean flow interactions are a sink for wavenumber 3 kinetic energy. In contrast, during SH summer wave–wave coupling between intermediate-scale transients and wavenumber 3 is sharply reduced compared to winter. This suggests that wave–wave interaction is an important component in the mechanism of the SH bimodality.

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Anthony R. Hansen and Alfonso Sutera

Abstract

The effect of the zonally asymmetric forcing due to topography on the low-frequency variability of the large-scale flow is investigated for Northern Hemisphere winter conditions. Extended general circulation model integrations are used in which the topographic heights are reduced.

The effect of reduced topographic heights is to reduce the mean persistence of recurrent regimes identified from the amplitude of the planetary waves with spatial scales comparable to the topography. The number of episodes of large wave amplitude and their anomaly patterns are affected very little. The impact of topography on the total gridpoint height variance includes two components. Decreased topographic heights lead to increased high-frequency eastward-traveling variance and decreased low-frequency variance. In addition, the regionalization of the Pacific and Atlantic storm tracks found in the control simulation diminishes as the topographic heights are reduced.

From the results the authors conclude that the occurrence of persistent regimes in the large-scale flow is linked to the presence of topographic forcing of sufficient amplitude but that the amplification mechanism of the planetary waves is not directly linked to the topographic forcing. Therefore, it appears that the topography plays a catalytic role in permitting longer persistence of a large-scale, amplified planetary wave flow regime.

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Anthony R. Hansen and Alfonso Sutera

Abstract

The probability density distribution of the speed, horizontal shear and vertical shear of the zonal-mean wind are computed from a 16-winter NMC dataset in a study designed to complement an earlier study of the planetary-scale wave amplitude probability density distribution. The speed of the zonal wind is found to have a probability density distribution that is unimodal both within the zone of the largest planetary wave amplitude (45°–70°N) and when averaged over the entire midlatitudes (25°–75°N). Unimodal distributions are also found for both the north–south shear of the zonal mean wind and the vertical shear of the zonal mean flow between 300 and 850 mb.

Lagged correlations between the zonal mean wind parameters and the wavenumber 2–4 amplitude are computed and found to be small at all lags. This suggests that the temporal variability of the planetary waves in the midlatitudes of the troposphere is not directly connected to the variability in the strength or shear of the zonal mean flow.

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Anthony R. Hansen and Alfonso Sutera

Abstract

The composite of large amplitude flow anomalies identified from extremely large amplitudes of the planetary-scale waves is examined in terms of the temporal and spatial evolution of both the large-scale flow and the storm tracks. The characteristic spatial patterns, growth and decay rates, and persistence characteristics that the individual large amplitude anomaly cases share come out naturally in the analysis.

The composite anomaly's growth and decay are very rapid, taking an average of only 4 days to develop local anomalies of 200–300 m. The spatial evolution of the flow suggests a rapidly growing standing wave over the North Pacific Ocean and North America. After a persistence of random duration (averaging 8.4 days), the composite anomaly's decay is accompanied by simultaneous retrogression of the pattern from western North America to eastern Asia and eastward progression of the pattern over Europe and western Asia. Substantial disruption of the Pacific storm track and enhancement of the Atlantic storm track accompanies the life cycle of this flow regime. A residual effect of the regime life cycle is a reduction in the low-level meridional temperature gradient, particularly over eastern Asia in the entry region of the Pacific jet stream.

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Anthony R. Hansen and Alfonso Sutera

Abstract

A preliminary study of the probability density distribution of the wavenumber 3 amplitude in midlatitudes of the Southern Hemisphere is undertaken with 4.25 years of 500 mb height data compiled by the European Centre for Medium-Range Weather Forecasts. The wavenumber 3 amplitude probability density appears to be bimodal during winter. Analogous results during the Southern Hemisphere summer reveal a unimodal wavenumber 3 amplitude probability density distribution with the single summer mode corresponding in value to the winter low amplitude mode.

The physical implications of the winter bimodality are examined to gain confidence in the result. Partitioning the data based on the two modes leads to a consistent picture of the large amplitude events in physical space. Synoptically, the large amplitude mode corresponds to “amplified waves” of broad extent. It is suggested that the SH winter time-mean eddies for wavenumbers greater than one are the statistical residue of the intermittent large-amplitude events. Individual Southern Hemisphere large amplitude events exhibit grid point height departures from zonal symmetry comparable to their Northern Hemisphere counterparts. In addition, the summer mean eddy field is very similar to the winter low amplitude mode's mean eddy field.

Examination of the time series of the wave 3 amplitude and phase during winter reveals that the more persistent of the individual large amplitude events exhibit relatively stationary phase lines, although different large amplitude events may have different phases. A remarkable feature of these time series is that certain of the more persistent events exhibit a sudden phase shift while the amplitude remains large with the phase being steady both before and after the shift.

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Anthony R. Hansen and Alfonso Sutera

Abstract

Recent studies of low-frequency variability have shown that at least two planetary-scale statistical flow regimes exist in the Northern Hemisphere winter circulation both in observations and in a general circulation model. This result was obtained from an analysis of a large-scale circulation index based on planetary-wave amplitude. In this paper, a 1200-day integration of the NCAR Community Climate Model (CCM0) in perpetual January mode is used as a case study to show that similar results in terms of multiple flow regimes can also be obtained from an empirical orthogonal function (EOF) analysis. Two modes are found in the probability density distribution in the subspace formed from the leading two EOFs of the model. There is an apparent correspondence between these modes and the two modes deduced from the previous wave-amplitude analysis.

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