EOF analysis of a time series with application to tsunami detection

Fragments of deep-ocean tidal records up to 3 days long belong to the same functional sub-space, regardless of the record’s origin. The tidal sub-space basis can be derived via Empirical Orthogonal Function (EOF) analysis of a tidal record of a single buoy. Decomposition of a tsunami buoy record in a functional space of tidal EOFs presents an efficient tool for a short-term tidal forecast, as well as for an accurate tidal removal needed for early tsunami detection and quantification [Tolkova, E., 2009. Principal component analysis of tsunami buoy record: tide prediction and removal. Dyn. Atmos. Oceans 46 (1–4), 62–82] EOF analysis of a time series, however, assumes that the time series represents a stationary (in the weak sense) process. In the present work, a modification of one-dimensional EOF formalism not restricted to stationary processes is introduced. With this modification, the EOF-based de-tiding/forecasting technique can be interpreted in terms of a signal passage through a filter bank, which is unique for the sub-space spanned by the EOFs. This interpretation helps to identify a harmonic content of a continuous process whose fragments are decomposed by given EOFs. In particular, seven EOFs and a constant function are proved to decompose 1-day-long tidal fragments at any location. Filtering by projection into a reduced sub-space of the above EOFs is capable of isolating a tsunami wave within a few millimeter accuracy from the first minutes of the tsunami appearance on a tsunami buoy record, and is reliable in the presence of data gaps. EOFs with ∼$\sim$3-day duration (a reciprocal of either tidal band width) allow short-term (24.75 h in advance) tidal predictions using the inherent structure of a tidal signal. The predictions do not require any a priori knowledge of tidal processes at a particular location, except for recent 49.5 h long recordings at the location.     

An experimental study of nonlinear baroclinic instability and mode selection in a large basin

This paper reports on two-layer rotating liquid experiments designed to study the behavior of non-linear baroclinic waves under conditions where the Rossby radius of deformation R_d is much smaller than the geometric length scale L imposed by the size of the laboratory apparatus. The apparatus is constructed to consistently simulate f-plane dynamics. When F = L²/R_d² > > 1, it is found that the unstable waves first encountered as friction is decreased have high frequencies, in accord with linear theory. As the friction parameter $\text{Q = 0.7 E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/R}{}_0$ (where E is the Ekman number and R₀ the Rossby number) is further decreased into the non-linear region, singlewave amplitude vacillation is observed. Generally, as Q decreases lower frequencies (and low wavenumbers) dominate the response, which ultimately becomes turbulent at values of Q of the order 0.1. This is contrary to the result expected from an extrapolation of linear theory. Further observations show that the finite-amplitude state is not unique: multi-equilibria are possible depending on the initial conditions.     

A parameter study of the mixed instability of idealized ocean currents

We investigate the nature of linear instabilities that can arise on eastward-flowing baroclinic currents similar to those found to serve as sites of strong eddy-mean flow interaction in certain mesoscale-resolution ocean circulation studies. The intent is to deduce the dependence of the linear instability mechanism — thought to be operative in some form in these simulations — on the internal parameters characterizing them. Following conventional practice, we adopt as our physical model the two-level quasigeostrophic potential vorticity equations which, in their linearized form, are solved numerically to yield the properties of the most unstable linear waves under a variety of mean flow and environmental conditions. The kinematic and dynamic features of the growing perturbations — preferred wavelength, growth rate and frequency, eddy-mean field energy transfers and vertical distribution of wave amplitude — are shown to be sensitive functions of our nondimensional parameters: $\text{(}\text{i}\text{) α = (}\text{U}{}_3\text{U}{}_1\text{)}$, the ratio of lower to upper level velocity scale amplitude; $\text{(}\text{ii}\text{) X = (}\text{R}{}_{\mathrm{<mtext>d</mtext>}}\text{L}\text{)}$, the ratio of the first baroclinic deformation radius to the meridional width of the jet; $\text{(}\text{iii}\text{) δ = (}\text{H}{}_1\text{H}{}_3\text{)}$, the resting layer depth ratio; and $\text{(}\text{iv}\text{) ? = (}\text{βL}{}^2\text{U}\text{)}$, an (inverse) Rossby number based on the northward gradient of the planetary vorticity (β). Viscous effects, although included in the analysis, are shown to be unimportant for values of frictional coefficients typical of recent eddy-resolving ocean model studies. Despite a strong dependence of the details of the linear instability mechanism on environmental factors, the associated unstable eigenmodes do have important structural similarities which are intimately connected with their ability to extract energy from the mean flow.     

Selective withdrawal of rotating stratified fluid

A simple theory and some experimental observations are presented of the transient withdrawal of rotating, stratified fluid in a field of gravity. The problem is confined to axisymmetric geometry and negligible viscosity. It is predicted that the withdrawal initially proceeds like non-rotating selective withdrawal, but at a time equal to $\text{3√}\text{3}\text{2?}$ there is a transition to a rotation-dominated selective withdrawal process which requires that fluid come from distances above and/or below the inlet given by the time-dependent formula $\text{(?Qt/2πr}{}_0\text{N)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Experimental observations are given which are in approximate agreement with the predictions.