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Carl Wunsch

Abstract

The time- and space-scale descriptive power of two-dimensional Fourier analysis is exploited to reanalyze the behavior of midlatitude variability as seen in altimetric data. These data are used to construct a purely empirical and analytical frequency–zonal wavenumber spectrum of ocean variability for periods between about 20 days and 15 yr and on spatial scales of about 200–10 000 km. The spectrum is dominated by motions along a “nondispersive” line, which is a robust feature of the data but for whose prominence a complete theoretical explanation is not available. The estimated spectrum also contains significant energy at all frequencies and wavenumbers in this range, including eastward-propagating motions, which are likely some combination of nonlinear spectral cascades, wave propagation, and wind-forced motions. The spectrum can be used to calculate statistical expectations of spatial average sea level and transport variations. However, because the statistics of trend determination in quantities such as sea level and volume transports depend directly upon the spectral limit of the frequency approaching zero, the appropriate significance calculations remain beyond reach, because low-frequency variability is indistinguishable from trends already present in the data.

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Carl Wunsch

Abstract

A recent paper by Hu et al. (https://doi.org/10.1126/sciadv.aax7727) has raised the interesting question of whether the ocean circulation has been “speeding up” in the last decades. Their result contrasts with some estimates of the lack of major trends in oceanic surface gravity waves and wind stress. In general, both the increased energy and implied power inputs of the calculated circulation correspond to a small fraction of the very noisy background values. An example is the implied power increase of about 3 × 108 W, as compared to wind energy inputs of order 1012 W. Here the problem is reexamined using a state estimate that has the virtue of being energy, mass, etc. conserving. Because it is an estimate over an entire recent 26-yr interval, it is less sensitive to the strong changes in observational data density and distribution, and it does not rely upon nonconservative “reanalyses.” The focus is on the energy lying in the surface layers of the ocean. A potential energy increase is found, but it is almost completely unavailable—arising from the increase in mean sea level. A weak increase in kinetic energy in the top layer (10 m) is confirmed, corresponding to an increase of order 1 cm s−1 yr−1 over 26 years. An estimate of kinetic energy in the full water column shows no monotonic trend, but the changes in the corresponding available potential energy are not calculated here.

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Carl Wunsch

Abstract

An infinitely deep stratified ocean on a equatorial beta plane is forced with a periodic wind system. The resulting linearized motion is shown to result in a deep cellular flow structure in rough agreement with recent observations. Because of the infinite depth, the vertical structure is dependent only on the horizontal structure and frequency of the wind-forced layer. The motion is a mechanism for carrying momentum downward from the surface. A western boundary is easily accommodated.

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Carl Wunsch

Abstract

Internal wave records from a variety of deep water locations in the North Atlantic have been reduced by common analysis methods in a search for systematic deviations from a universal spectral model. Such inhomogeneities are probably necessary conditions for sources and sinks of the motion. For a number of reasons, only records at 2000 m and below were used. Real variations in energy level of up to an order of magnitude were found, but the only clear inhomogeneities are associated with bottom topography, especially in those records obtained near Muir seamount. The effects, if any, on the internal wave field by the large velocity and shear of the Gulf Stream region are weak. Apparent topographic sources are inconspicuous at very short distances, suggesting a very rapid, nonlinear recovery of the spectrum to an equilibrium form.

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Carl Wunsch

Abstract

Difficulties remain with theoretical explanations of the apparent reduced zonal sea surface temperature gradient in the tropical Pacific of the Pliocene. One favored hypothesis is that it was a “permanent El Niño” state, with the warm phase of ENSO remaining fixed over millions of years. Here, an alternative is suggested—that there was a “perpetually running ENSO” with a shorter return time than is observed today, and that the apparently reduced zonal gradient is an alias–rectification of a high-frequency signal governed by the growth patterns of the foraminifera used to provide proxy temperatures. The hypothesis is probably testable in the modern ocean with comparatively modest measurements of foraminifera behavior in time.

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Carl Wunsch

Abstract

A model of the Atlantic has been formulated that combines ordinary quasi-geostrophic constraints (based upon the dynamic method and Ekman layer) with a great variety of additional information available about the time-average ocean circulation. The goal is to combine very diverse data types and beliefs and to be able to test for compatibility and incremental usefulness as a way around the paucity of conventional data, a lack of which otherwise greatly hinders determination of the circulation.

The approach is axiomatic. Such a model is based here upon the use of linear inequality constraints, which permit the combination of the dynamic method with “core layer”-like constraints, as well as observations of deep water velocities, overflow transports and the like. The model is then exploited to find absolute bounds (maxima and minima) upon the annual mean and seasonal meridional fluxes of heat and the maximum rate of tropical near-surface upwelling. Some latitudes of nearly vanishing mean meridional heat flux are just possible within the imposed constraints, but it appears impossible to reverse the sign of the heat flux at any latitude except in winter. The latitude of maximum possible annual-mean poleward heat flux is 40°N. Based upon a radiocarbon box model, the value of tropical upwelling is much less than published values. The model is very “slack”, i.e., most properties are locally determined rather than being forced by distant constraints.

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Carl Wunsch

Abstract

The dominant contributor to the random error of an altimetric satellite system is the long wavelength uncertainty in the orbital radius. It is shown that calibration by a comparatively modest tide gauge system can drastically reduce the overall error in global estimates of large-scale oceanic variability. The procedure used is a form of optimal estimation. Absolute (time average) altimetric calibration is much more difficult because it requires absolute calibration of the tide gauge positions (in three dimensions) but the error reduction process would be the same.

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Carl Wunsch

Abstract

No abstract available.

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Carl Wunsch

Abstract

The irregular space-time sampling of any finite region by an orbiting satellite raises difficult questions as to which frequencies and wavenumbers can be determined and which will alias into others. Conventional sampling theorems must be extended to account for both irregular data distributions and observational noise—the sampling irregularity making the system much more susceptible to noise than in regularly sampled cases. The problem is formulated here in terms of least-squares and applied to spacecraft in 10-day and 17-day repeating orbits. The “diamond-pattern” laid down spatially in such repeating orbits means that either repeat period adequately samples the spatial variables, but the slow overall temporal coverage in the 17-day pattern leads to much greater uncertainty than in the shorter repeat cycle. The result is not definitive and it is not concluded that a 10-day orbit repeat is the most appropriate one, A major conclusion however, is that different orbital choices have potentially quite different sampling characteristics which need to be analyzed in terms of the spectral characteristics of the moving sea surface. Conclusions drawn from model assimilation studies need to be placed in a context of the reality of their spectral content via-àvis the ocean.

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Carl Wunsch

Abstract

The modal decomposition, proportional amplitudes, and lateral spatial scale of baroclinic motions in the North Atlantic Ocean are described as determined from more than 20 years of moored instrument data. The subtropical and subpolar gyres emerge naturally as regions of distinct energy levels, in the ratio of potential to kinetic energy, and in horizontal wavelength. Data in other ocean basins prove too sparse to use.

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