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- Author or Editor: Peter Müller x
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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.
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.
Abstract
The radiative balance equation describes the evolution of the internal wave action density spectrum n (k) in response to propagation, generation, nonlinear transfer, dissipation, and other processes. Dissipation is assumed to be due primarily to wave breaking, either by shear or gravitational instability. As part of the Internal Wave Action Model (IWAM) modeling effort, a family of dissipation functions is studied that is to account for this dissipation by wave breaking in the radiative balance equation. The dissipation function is of the quasi-linear form S diss = −γ (k, Ri−1) n(k), where the dissipation coefficient γ depends on wavenumber k and inverse Richardson number Ri−1. It is based on the dissipation model of Garrett and Gilbert (1988) and contains three free adjustable parameters: c 0, p, and q. To gain insight into the role that each of the free parameters plays in the dissipative decay of the wave spectrum, we first consider simple examples that can be solved analytically: the response to homogeneous and stationary forcing, the free temporal decay of a Garrett and Munk spectrum, and the spatial decay of a monochromatic and bichromatic spectrum. Then the more complex problem of the reflection of an incoming Garrett and Munk spectrum off a linear slope is solved numerically. In these examples, the parameter c 0 determines how rapidly the spectrum decays in space or time, p the form or shape of this decay, and q the relative decay of different wavenumbers. These dependencies are sufficiently strong to suggest that the free parameters can eventually be calibrated by comparing solutions of the radiative balance equation with observations, using inverse techniques.
Abstract
The radiative balance equation describes the evolution of the internal wave action density spectrum n (k) in response to propagation, generation, nonlinear transfer, dissipation, and other processes. Dissipation is assumed to be due primarily to wave breaking, either by shear or gravitational instability. As part of the Internal Wave Action Model (IWAM) modeling effort, a family of dissipation functions is studied that is to account for this dissipation by wave breaking in the radiative balance equation. The dissipation function is of the quasi-linear form S diss = −γ (k, Ri−1) n(k), where the dissipation coefficient γ depends on wavenumber k and inverse Richardson number Ri−1. It is based on the dissipation model of Garrett and Gilbert (1988) and contains three free adjustable parameters: c 0, p, and q. To gain insight into the role that each of the free parameters plays in the dissipative decay of the wave spectrum, we first consider simple examples that can be solved analytically: the response to homogeneous and stationary forcing, the free temporal decay of a Garrett and Munk spectrum, and the spatial decay of a monochromatic and bichromatic spectrum. Then the more complex problem of the reflection of an incoming Garrett and Munk spectrum off a linear slope is solved numerically. In these examples, the parameter c 0 determines how rapidly the spectrum decays in space or time, p the form or shape of this decay, and q the relative decay of different wavenumbers. These dependencies are sufficiently strong to suggest that the free parameters can eventually be calibrated by comparing solutions of the radiative balance equation with observations, using inverse techniques.
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.
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.
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.
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.
Abstract
The scattering of oceanic internal gravity waves off random bottom topography is analyzed under the assumptions that (i) the height of the topography is smaller than the vertical wavelength and (ii) the slope of the topography is smaller than the wave slope. For each frequency, scattering redistributes the incoming energy flux in horizontal wavenumber space. The scattered wave field approaches an equilibrium state where the energy flux is equipartitioned in horizontal wavenumber space. For incoming red spectra, this implies a transfer from low to high wavenumbers. For typical internal wave and bottom spectra, about 6.8% of the incoming energy flux is redistributed. While this might be less than the flux redistribution caused by reflection off a critical slope, the scattering process transfers the energy flux to higher wavenumbers than the reflection process. Scattering might thus be equally or more efficient than reflection in causing high shears and mixing near the bottom.
Abstract
The scattering of oceanic internal gravity waves off random bottom topography is analyzed under the assumptions that (i) the height of the topography is smaller than the vertical wavelength and (ii) the slope of the topography is smaller than the wave slope. For each frequency, scattering redistributes the incoming energy flux in horizontal wavenumber space. The scattered wave field approaches an equilibrium state where the energy flux is equipartitioned in horizontal wavenumber space. For incoming red spectra, this implies a transfer from low to high wavenumbers. For typical internal wave and bottom spectra, about 6.8% of the incoming energy flux is redistributed. While this might be less than the flux redistribution caused by reflection off a critical slope, the scattering process transfers the energy flux to higher wavenumbers than the reflection process. Scattering might thus be equally or more efficient than reflection in causing high shears and mixing near the bottom.
