Steven D. Meyers

An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves

Abstract Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an “instantaneous” estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumber, possibly due to interaction with the basin boundaries.

ENSO Effects on Gulf of Alaska Eddies

Abstract Generation and propagation of eddies in the coastal regions of the eastern Gulf of Alaska are examined based on ouput from a numerical ocean model. Results from a 1/8° six-layer isopycnal, wind-forced Pacific basin model are examined within the Gulf of Alaska during the 14-yr period starting in January 1981. Interannual variability in the upper ocean coastal circulation in the Gulf of Alaska is linked to the El Nino–Southern Oscillation phenomenon in the tropical Pacific Ocean, via coastal Kelvin waves and atmospheric teleconnections. El Nino events destabilize the Alaska Current by enhancement of the velocity shear in the vertical. The instability ultimately results in the formation of multiple strong anticyclonic eddies along the coast, which slowly propagate into the Gulf of Alaska where they can survive for more than 1 yr. A typical value for the diameters of the anticyclonic eddies is 200 km in the data and in the model. These eddies are strongly baroclinic, with a typical value for the velo...

ENSO and eddies on the southwest coast of Mexico

TOPEX/POSEIDON and ERS-2 (T/ERS) sea surface height altimeter observations and the Naval Research Laboratory Layered Ocean Model (NLOM) are used to study the circulation along the southwest coast of Mexico. The results of this research indicate that strong El Nino/Southern Oscillation (ENSO) warm phase Kelvin waves (KW) destabilize the upper ocean circulation. The effect of ENSO appears as three distinct stages. First, a coastal jet characterized by strong vertical shear flow develops. Second, the shear flow strengthens, increasing its horizontal dimension and the amplitude of its oscillations. Finally, the jet becomes unstable and breaks into anticyclonic eddies, which separate from the coast and drift southwestward. The genesis and strengthening of the jet is due to the simultaneous occurrence of the poleward-flowing currents along the southwest coast of Mexico and the poleward circulation associated with ENSO downwelling KW.

Chaos and mixing in a geostrophic flow

Experiments on Rossby waves on an azimuthal jet in a rapidly rotating annular tank reveal a striking barrier to mixing across the jet. A model based on the experiments assumes a two‐dimensional incompressible flow described by a time‐dependent streamfunction consisting of azimuthally propagating waves on a narrow jet. When there is only one wave, all Lagrangian particle trajectories are closed in the appropriate reference frame. When two independent waves are present, some trajectories are chaotic, and the size of the chaotic sea grows as the amplitude of the second wave is increased; however, at least one barrier to global transport—an invariant surface—prohibits trajectories from crossing the jet. The addition of a third wave is found to break the barrier only if the wave amplitudes exceed the width of the jet. In the experiment, the wave amplitude is typically about one‐half the jet width, and the barrier to mixing persists even at the highest accessible Reynolds numbers.

Annual and interannual sea level variations in the Indian Ocean from TOPEX/Poseidon observations and ocean model simulations

Sea level variations relative to a 4-year mean in the Indian Ocean north of 10°S are examined during 1993–1996 using both a numerical reduced gravity model with realistic coastline geometry and wind stress and sea level measurements from the TOPEX/Poseidon altimeters. The annual signal is found to be composed of propagating as well as nonpropagating features. The propagation speeds in the model and altimetry generally agree to within 25% or less. Complex empirical orthogonal function (CEOF) decomposition yields a separation between the annual and semiannual cycles (46 and 30% of the respective variance for the model, and 40 and 26% for the altimetric measurements, respectively). The propagation of these signals across the ocean basin is indicated by the spatial phase functions. Both temporal phase functions are steady for the annual cycle, though the amplitudes are modulated in time. The results for the semi-annual cycles are similar, but the temporal phase functions are disrupted for ∼12 months starting in 1994. This may be due to an unusually strong monsoon during that time. The correlation between model sea level variation and those measured by altimetry is highly variable in both space and time. Low-frequency filtering of the sea level anomalies, obtained by summing the two largest CEOF modes (the annual and semiannual cycles), improves the correlation. The filtered anomalies correlate in time as high as 0.9 in the western Arabian Sea and as high as 0.7 south of the equator and in the eastern Bay of Bengal. There are pockets of poor correlation (as low as −0.4) in the eastern Arabian Sea, central Bay of Bengal, and central equatorial region. These areas tend to contain recurring Rossby wave interactions as represented by the 1.5-layer model. Each area is associated with a “phase nexus” (analogous to an amphidromic point in tidal theory) or a strong gradient of the model spatial phase functions. The spatial correlation between the filtered anomalies is typically 0.6 over much of the observation period but contains unexplained declines as low as 0.2 during a few months in both 1995 and in 1996.

Observations of currents on the West Florida Shelf Break

Year-long measurements by five acoustic Doppler current profilers moored across the central West Florida Shelf (WFS) and shelf break reveal new information on the local velocity structure and its temporal evolution. The moorings were between the 30 and 300 m isobaths. At depths greater than about 100 m the currents were sometimes directly affected by the deep ocean. During the measurement period the Loop Current (LC) directly impacted the central WFS three times, amounting to a total of about 13% of the year. For the remainder of the year the shelf break currents had equal likelihood of flowing northward or southward. Northward currents achieved over 70 cm/s and the southward currents (driven by the LC) achieved 120 cm/s. Neighboring instruments recorded strong (∼30 cm/s) currents flowing in opposite directions. Current reversals, in one case totally nearly 100 cm/s within a few days, were also found.

Eddies in the eastern Gulf of Alaska from TOPEX/POSEIDON altimetry

Eddy activity in the Gulf of Alaska (GOA) is evidenced to fluctuate with the El Nino-Southern Oscillation (ENSO) cycle. Altimetry from TOPEX/POSEIDON is used to study eddy formation along a single descending track in the far eastern GOA from late 1992 through late 1998. The track is sampled between 45°N and 60°N, where it is roughly parallel to the eastern boundary. The geoid and mean currents are removed from the data through extraction of the temporal mean at each point. The resulting anomalies are passed through a matched filter designed to detect Gaussian signals embedded in noise. The filter is optimized to detect eddies with amplitude ≳10 cm and diameters roughly 50–350 km. Both anticyclonic and cyclonic structures are examined. The distribution of eddies in space is similar for both anticyclonic and cyclonic eddies, with most occurring between 50°N and the northern limits of the GOA. Few eddies of either sign were found south of 50°N. Anticyclonic eddies are stronger and have a broader distribution of amplitudes (typically 5–30 cm) compared to cyclonic features, which are more symmetrically distributed over 5–15 cm. The detection of weak (≃15 cm) eddies is sensitive to the filter threshold, but detection of larger-amplitude eddies is robust. The average amplitude of anticyclonic eddies increases following the 1993, 1994/1995, and 1998 El Nino events. Eddy amplitude appears to vary with ENSO strength: the strongest eddies detected form in early 1998. These results support previous numerical studies of eddy development in the eastern GOA.

Cross-Frontal Mixing in a Meandering Jet

Abstract A Gulf Stream-like meandering current is kinematically modeled using a streamfunction ψ = Uλ(1 − tanh[(y − yc)/λ cos(α)]. Under suitable parameter values a “front” exists along the velocity maximum across which there is no transport, but with mixing occurring on either side. An analogous barrier exists in the Gulf Stream but appears to fade with depth. The conditions for mixing across the model front are studied using the Chirikov overlap criterion, which indicates the front breaks down for meander amplitude above a critical threshold that is inversely dependent on the ratio of meander phase speed and current speed, c/U. It is suggested that the increase in cross-frontal mixing in the deeper levels of the Gulf Stream is the result of current meandering and the decrease of current velocity with depth. The mechanism for this is interaction of different meander modes traveling along the Gulf Stream. These ideas are shown to be consistent with field measurements of tracers in the ocean.

A numerical simulation of residual circulation in Tampa Bay. Part I: Low-frequency temporal variations

The residual (time-average) salinity and circulation in a numerical ocean model of the Tampa Bay estuary are shown to experience significant temporal variation under realistic forcing conditions. A version of the Estuarine Coastal Ocean Model developed for Tampa Bay with 70 by 100 horizontal grid points and 11 sigma levels is examined for the years 2001–2003. Model output variables are averaged over the entire time of the simulation to generate long-term residual fields. The residual axial current is found to be dominated by the buoyancy-driven baroclinic circulation with an outflow (southwestward) at the surface and to the sides of the shipping channel, and an inflow (northeastward) usually occurring subsurface within or above the shipping channel. Averages over 30 d are used to examine variations in the residual fields. During the simulation the average surface salinity near the head of Tampa Bay varies with the freshwater inflow, from 12‰ to 33%. At the bay mouth salinity varies from 30%. to 36%.. A localized measure of the baroclinic circulation in the shipping channel indicates the residual circulation can vary strongly, attaining a magnitude triple the long-term mean value. The baroclinic circulation can be disrupted, going to near zero or even reversing, when the buoyancy-driven flow is weak and the surface winds are to the northeast. Three time periods, representing different environmental conditions, are chosen to examine these results in detail. A scaling argument indicates the relative strength of buoyancy versus wind as ΔρgH2(LCDω2)−1, where δρ is head-to-mouth density difference across the bay,g is gravitational acceleration,H is depth,L is bay length,CD is the surface wind drag coefficient, andw is wind speed. Tampa Bay is usually in the buoyancy dominated regime. The importance of winds in the weak-buoyancy case is demonstrated in an additional simulation without wind stress.

Interdecadal Variability in a Numerical Model of the Northeast Pacific Ocean: 1970–89

Abstract Variations in the thermocline depth of the northeast Pacific Ocean during 1970–1989 are investigated using a reduced-gravity numerical model forced by the local surface wind stress and at the southern land-ocean boundary by a coastal Kelvin wave signal. Three experiments are presented with forcings by wind only, Kelvin wave only, and a combination of both. The wind forcing generates an anticyclonic gyre circulation with mostly annual variations. The Kelvin waves along the coast excite Rossby waves that propagate into the basin interior, producing changes in upper-layer thickness (related to changes in thermocline depth) that last for years after the Kelvin signal has passed. Two sequential upwelling Kelvin waves in 1973 and 1975 produce upwelling Rossby waves that reduce the mean upper-layer thickness by approximately 10–20 m during 1976. This shift is reinforced by later upwelling events lasting until the early 1980s. The authors present a new hypothesis that the previously known climate shift o...