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Peter Müller

Abstract

Coherence maps are a useful tool to study the oceanic response to atmospheric forcing. For a specific frequency band these maps display the coherence between the oceanic current (or pressure) at a single mooring location and the atmospheric forcing field at other locations as a function of separation. This paper calculates such coherence maps from a simple linear quasigeostrophic model forced by a statistically stationary and homogeneous wind field. The calculated coherence maps show values less than one. Such values are not due to the presence of noise but are a consequence of the ocean being forced at many locations. The maps also show characteristic patterns with maxima either at the mooring location or away from it. The locations of the maxima do not indicate the locations of the forcing but instead reflect the scales of the atmospheric forcing spectrum and of the Green’s function of the potential vorticity equation. Coherence maps can be used to estimate the Green’s function in a multiple regression analysis. The presence of noise or nonlinearities in the system can be inferred from the multiple coherence, which is a number. Emphasis is on understanding the information content of coherence maps, not on reproducing observed maps. The results can be generalized to other systems where response and forcing are related by a Green’s function.

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Peter Müller
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Peter Müller
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Peter Müller
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Peter Müller
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Peter Müller
and
Claude Frankignoul

Abstract

To assess the role of direct stochastic wind forcing in generating oceanic geostrophic eddies we calculate analytically the response of a simple ocean model to a realistic model wind-stress spectrum and compare the results with observations. The model is a continuously stratified, β-plane ocean of infinite horizontal extent and constant depth. All transfer and dissipation processes are parameterized by a linear scale-independent friction law (Rayleigh damping). The model predictions that are least sensitive to this parameterization, the total eddy energy and the subsurface displacement, are in good agreement with observations in mid-ocean regions far removed from strong currents. Properties that depend crucially on the parameterization of nonlinearities and topographic effects are not well reproduced. Observed coherences and seasonal modulations provide direct evidence of wind forcing at high frequencies where motions have little energy. Direct evidence at the more energetic low frequencies will be difficult to detect because the expected coherences are small. Altogether, the present results suggest that direct wind forcing may well be the dominant forcing mechanism for central ocean eddies.

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Niklas Schneider
and
Peter Müller

Abstract

We describe the meridional and seasonal structures of daily mean mixed-layer depth and its diurnal amplitude and their relation to atmospheric fluxes by compositing mixed-layer depth estimates derived from density observations. The diurnal mean mixed-layer depth shows a ridge at the equator, troughs, which vary seasonally in intensity, at 10° to 15°N and 5° to 10°S, and a trough appearing just north of the equator in the second half of the year. This is in contrast to the ridge-trough structure of the top of the main thermocline, which reflects the dynamic topography associated with the equatorial current system. The diurnal amplitude is significantly different from zero for most latitudes year-round, indicating that the diurnal cycle of mixed-layer depth is a widespread phenomenon. For sufficiently strong heating, both the mixed-layer depth and its diurnal amplitude are significantly correlated with Monin-Obukhov length scales based on the mean net heat flux, mean wind stress, and mean shortwave radiation. This suggests a possible parameterization of the mixed-layer depth and diurnal amplitude in terms of the mean atmospheric fluxes for meridional scales of a few degrees and seasonal time scales.

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Claude Frankignoul
and
Peter Müller

Abstract

Stochastic fluctuations in the buoyancy flux at the air-sea interface create density anomalies in the oceanic surface layer, which drive quasi-geostrophic motions in the ocean interior. The efficiency of this forcing mechanism is evaluated by comparison with wind-stress forcing. Stochastic buoyancy forcing is found to be always negligible in the wavenumber-frequency range of oceanic geostrophic eddies. The effect of mass exchange anomalies at the surface is also found to be negligible. The conclusions seem applicable to time scales up to centuries.

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Claude Frankignoul
and
Peter Müller

Abstract

The quasi-geostrophic response of the ocean to stochastic forcing by wind stress and atmospheric pressure is investigated using a linear, continuously stratified, β-plane oceanic model with a flat bottom. We consider a spectral representation of the forcing and response fields, and we estimate the oceanic response using a vertical normal mode expansion. Model spectra of the wind stress, wind stress curl and surface pressure fields are constructed. In the wavenumber-frequency range of quasi-geostrophic eddies, the observations suggest that because of their short correlation time scale, the forcing fields are, to a reasonable approximation, white in frequency space and symmetric in wavenumber space. Forcing by the wind stress has the dominant role. The oceanic response can be off-resonant or resonant. In the off-resonant case, we predict oceanic wavenumber-frequency response spectra. In case of resonance we estimate total energy transfer rates by integrating the oceanic response over depth and wavenumber (in the range 2π/4000 km−1–2π/50 km−1) and we distinguish between the barotropic and the total baroclinic response, the latter being obtained by summing the contribution of all baroclinic modes.

The barotropic response is resonant at practically all eddy frequencies, and the baroclinic response is resonant at frequencies smaller than the maximum frequency of the first baroclinic Rossby wave. In midlatitudes, we find comparable energy input rates into barotropic and baroclinic modes, of the order of 3 × 10−4 W m−2. In high latitudes the input is comparable for barotropic Rossby waves and smaller for baroclinic ones. The total energy input rate by resonant forcing is only one order of magnitude smaller than the energy input rate from the mean atmospheric circulation into the general oceanic circulation. It is smaller, but comparable with the rate of energy conversion from the mean oceanic circulation into quasi-geostrophic eddies by barotropic and baroclinic instabilities. At medium and high frequencies, the baroclinic response is off-resonant. The model predicts red frequency spectra that are consistent with temperature observations in the central North Pacific. In particular, the seasonal variability of the observed eddy field is reproduced. A comparison with observations in the western North Atlantic also suggests that local stochastic forcing by the atmosphere is an important generating mechanism for the eddies in regions of low eddy activity.

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Jay McCreary
and
Peter Müller
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