Time Series Of Surface Elevation Research Articles

Measurements of a Barotropic Planetary Vorticity Mode in an Eddy-Resolving Quasi-geostrophic Model Using Acoustic Tomography

Abstract An acoustic source and receiver are placed at 800 m depth and are separated by 4000 km in a two-layer, steady-wind driven, flat bottom eddy-resolving quasi-geostrophic circulation model. Time series of sea surface elevation and upper and lower layer meridional currents are generated for comparison against a series of acoustic travel time. The spectra of the time series exhibit a broad mesoscale peak neat a period of 40 days. The spectrum of the acoustic travel time contains a significant peak which is not present in the spectra of the point measurements, due to a resonant barotropic osci11ation with a period of 29.0 days. In this numerical model, basin-scale tomographic measurements are a useful method of sensing the large-scale resonant barotropic oscillations because the tomographic system attenuates the “noise” from the mesoscale.

Formulation of a linear three‐dimensional hydrodynamic sea model using a Galerkin‐eigenfunction method

AbstractThe three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B‐splines.Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no‐slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty‐five B‐splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.Calculations show that in the case of a no‐slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin‐eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B‐splines, requires an expansion of the order of thirty‐five spline functions in order to obtain the same accuracy.Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no‐slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in the no‐slip model.

Removing Tidal-Period Variations from Time-Series Data Using Low-Pass Digital Filters

Abstract Several low-pass, digital filters are examined for their ability to remove tidal Period Variations from a time-series of water surface elevation for San Francisco Bay. The most efficient filter is the one which is applied to the Fourier coefficients of the transformed data, and the filtered data recovered through an inverse transform. The ability of the filters to remove the tidal components increased in the following order: 1) cosine-Lanczos filter, 2) cosine-Lanczos squared filter; 3) Godin filter; and 4) a transform fitter. The Godin fitter is not sufficiently sharp to prevent severe attenuation of 2–3 day variations in surface elevation resulting from weather events.

Estimation of scalar ocean wave spectra by the maximum entropy method

This paper describes the estimation of ocean wave spectra with the maximum entropy method. This method is based on an autoregressive model for the time series of sea surface elevation, and gives an all-pole estimate. The wave series are also prefiltered to introduce one zero in the spectral estimate. The methods are successfully applied to estimate the spectra of some typical wave series, requiring between 10 and 30 parameters. Our comparison with conventional spectral estimates also show that the new methods give good estimates of the spectral moments, that is important because the moments are parameters in a statistical description of the sea surface. The algorithms involved are well suited for realtime estimation of high-resolution wave spectra.