Semidiurnal M2 Research Articles

Effect of critical latitude and seasonal stratification on tidal current profiles along Ronne Ice Front, Antarctica

The ice front region of Ronne Ice Shelf lies near the critical latitude of the semidiurnal M2 tide, the principal tidal constituent in the southern Weddell Sea. Here the Coriolis frequency almost equals the M2 tidal frequency, resulting in a strong dependence of the M2 tidal currents on depth and stratification and a boundary layer that can occupy the entire water column. Using data from four long‐term moorings along Ronne Ice Front, we confirm the presence of strongly depth‐dependent semidiurnal tidal currents and their sensitivity to changes in stratification. The time series show dramatic seasonal changes in tidal current profiles and significant interannual variability. During periods of stratification, the amplitude of the semidiurnal tides in the mid–water column shows a twofold increase and, despite being several kilometers offshore from the ice front, the tidal currents clearly show a second boundary layer originating from the adjacent ice shelf base. Together, these two boundary layers occupy most of the water column, up to 600 m deep, until intense sea ice formation and the production of High‐Salinity Shelf Water erodes the vertical stratification. During winter when homogeneous conditions prevail, a single bottom boundary layer occupies the entire water column at some locations. This strong seasonality and sensitivity of the M2 tidal current to stratification highlights the difficulties of interpreting current data from short‐term moorings while demonstrating that it is the best indicator for characterizing changes in stratification after direct observations of density variations.

Numerical Modeling of Suspended Sediment Transport in the Gulf of Kachchh Including Kandla Creek, West Coast of India

A depth-averaged numerical model has been developed to study tidal circulation and suspended sediment transport in the Gulf of Kachchh including Kandla creek, west coast of India. The resolution of the model is taken as 750 m × 750 m, which is found to be adequate for the gulf region. However, this resolution could not produce the realistic circulation pattern and suspended sediment concentration in the Kandla creek region. There is a major seaport at Kandla which serves as the sea gate to northwest India. Therefore, a 2-D fine resolution (75 m × 75 m) model for Kandla creek has been developed and coupled with the coarser gulf model to compute the flow features in the creek region. The model dynamics and basic formulation remain the same for both the gulf model and the creek model. The models are barotropic, based on shallow water equations, and neglect horizontal diffusion and wind stress terms in the momentum equations. The models are fully nonlinear and use a semiexplicit finite difference scheme to solve mass, momentum, and advection-diffusion equations in a horizontal plane. The tide in the gulf is represented in the model by the semidiurnal M2 constituent mainly. In this study, no fresh water discharge conditions have been considered so the results are appropriate for the dry season. Numerical experiments are carried out to study the circulation and suspended sediment concentrations in the gulf and the creek regions. The computed results are validated with the available observations.

Evidence of strong inertia‐gravity wave activity during the POMME experiment

The purpose of this paper is to characterize inertia‐gravity waves (IGW) activity and to investigate the variability of these waves in relationship to atmospheric forcing and larger‐scale motions. To this aim, we analyzed Eulerian measurements of horizontal currents and temperature collected over 1 year during the Programme Océan Multidisciplinaire Méso Echelle (POMME). We focused on the main frequency components of the IGW spectrum, namely the inertial frequency f and the semidiurnal frequency M2. Time evolution of the relative energy of these two components gave evidence of isolated events of high intensity. We performed a detailed analysis of these events and identified mechanisms of generation of these waves. Localized spots of intense, near‐inertial IGW were observed in winter. During the mixed layer deepening, one event was correlated with plume‐like structures resulting from peaks of intense surface cooling. This suggests a local generation process driven by strong downward vertical motions. Instead, other events of strong IGW could be related to submesoscale features, characteristic of a frontal region, in particular, wave trapping within anticyclonic eddies. In contrast, a downward energy propagation down to about 500 m below the mixed layer was isolated after a stormy period. Eventually, internal tidal beams, possibly generated at a nearby seamount, intermittently crossed the mooring, though less energetically than the previous events. Last, we estimated the eddy diffusivity from the velocity vertical shear. Large variations were obtained, from 10−6 m2/s up to 10−3 m2/s, consistent with the intense events previously isolated.

On the fluctuations and vertical structure of the shelf circulation off Walvis Bay, Namibia

Temporal variations of the current field on the shelf of the South East Atlantic off Walvis Bay were studied during austral summer and fall by moored current profiler and temperature-salinity recorder located on the shelf 20 nm off Walvis Bay, Namibia. Spatial and temporal variations of the wind field in the South East Atlantic were investigated by 3-day averaged wind fields measured by the QuikSCAT satellite. The local wind was provided by a time series of hourly wind vectors measured on a moored buoy off Swakopmund. The significant tidal motion on the shelf off Walvis Bay is composed of the anticlockwise rotating barotropic semidiurnal constituents M2 and S2. The tidal currents are described to a first order by a barotropic deep ocean Kelvin wave. The land-sea breeze forces anticlockwise rotating diurnal variations of the current in the surface mixed layer and an opposite directed current below the thermocline, which compensates the mass flux normal to the coast in the surface layer. Most of the energy of the current fluctuations were concentrated around the local inertial period of T i = 30.7 h . These fluctuations consisted of at least four significant anti-clockwise rotating vertical modes with amplitudes ranging between 10 and 20 cm/s. On a large scale the amplitudes of inertial motions correlate with the wind fluctuations but locally the motions consist of a superposition of locally wind forced inertial oscillations and inertial waves generated at larger distances as well near the surface as close to the bottom. The vertical structure of the inertial motion suggests that it could be a possible candidate for mixing in the bottom boundary layer by differential advection. Coastal trapped waves of horizontal mode number less that four were observed at periods of about 7 days. The mean cross shelf circulation consisted of a two cell structure. The upper cell was made of the Ekman offshore current and a compensating onshore current at intermediate depth below the thermocline. The lower cell consisted of an offshore current in the bottom layer below 80 m depth and was closed by the onshore current in the intermediate depth range. The cross shelf circulation controlled the fraction of ESACW on the shelf water mass. The long shelf circulation consisted in the surface mixed layer of an equatorward coastal jet driven by the local meridional wind stress and an almost barotropic poleward counter current appearing partly as free Kelvin wave emanating from the Angola-Benguela front and as coastal counter current forced by the local negative curl of the wind stress. The longshore current controlled the fraction of the SACW on the shelf water mass, which increased continuously between austral summer and fall.

Barotropic Tide in the Northeast South China Sea

A moored array deployed across the shelf break in the northeast South China Sea during April-May 2001 collected sufficient current and pressure data to allow estimation of the barotropic tidal currents and energy fluxes at five sites ranging in depth from 350 to 71 m. The tidal currents in this area were mixed, with the diurnal O1 and K1 currents dominant over the upper slope and the semidiurnal M2 current dominant over the shelf. The semidiurnal S2 current also increased onshelf (northward), but was always weaker than O1 and K1. The tidal currents were elliptical at all sites, with clockwise turning with time. The O1 and K1 transports decreased monotonically northward by a factor of 2 onto the shelf, with energy fluxes directed roughly westward over the slope and eastward over the shelf. The M2 and S2 current ellipses turned clockwise and increased in amplitude northward onto the shelf. The M2 and S2 transport ellipses also exhibited clockwise veering but little change in amplitude, suggesting roughly nondivergent flow in the direction of major axis orientation. The M2 energy flux was generally aligned with the transport major axis with little phase lag between high water and maximum transport. These barotropic energy fluxes are compared with the locally generated diurnal internal tide and high-frequency internal solitary-type waves generated by the M2 flow through the Luzon Strait.

Tidal analysis of high and low water data

The harmonic analysis method based on high and low water levels is discussed in this paper. In order to make full use of the information of high and low water observations (the time derivative of water level at the observation time is zero), the weight coefficient, w, is introduced to control the importance of the part related to this information in the error formula. The major diurnal constituents, O1 and K1, and semi-diurnal constituents, N2, M2 and S2 are selected directly from the monthly data analysis, and some other important constituents, P1 v 2 and K2, are included as the inferred constituents. The obtained harmonic constants of the major constituents are very close to those obtained from the analysis of hourly data, and this shows that high and low water data can be used to extract tidal constants with high accuracy. The analysis result also shows that the inference and the weighting coefficient are important in the high and low water data analysis, and it is suggested that w≥l should be taken in monthly high and low water data analysis. This analysis method can be used directly to analyze altimetric data with w=0.

A modeling study of the Satilla River estuary, Georgia. I: Flooding-drying process and water exchange over the salt marsh-estuary-shelf complex

The flooding-drying process over the intertidal zone of the Satilla River estuary of Georgia was examined using a three-dimensional (3-D) primitive equations numerical model with Mellor and Yamada's (1982) level 2.5 turbulent closure scheme. The model was forced by the semi-diurnal M2, S2, and N2 tides and freshwater discharge at the upstream end of the estuary. The intertidal salt marsh was treated using a 3-D wet-dry point treatment technique that was developed for the σ-coordinate transformation estuary model. Good agreement was found between model-data comparison at anchor monitoring sites and also along the estuary that suggested that the model provided a reasonable simulation of the temporal and spatial distribution of the 3-D tidal current and salinity in the Satilla River estuary. Numerical experiments have shown that the flooding-drying process plays a key role in the simulation of tidal currents in the main river channel and in water transport over the estuarine-salt marsh complex. Ignoring this process could lead to a 50% under-estimation of the amplitude of tidal currents. The model results also revealed a complex spatial structure of the residual flow in the main channel of the river, with characteristics of multiple eddy-like cell circulations. These complicated residual currents are formed due to tidal rectification over variable topography with superimposition of inertial effects, asymmetry of tidal currents, and baroclinic pressure gradients. Water exchanges over the estuary-intertidal salt marsh complex are asymmetric across the estuary, and tend to vary periodically on the northern side while quickly washing out of the marsh zone on the southern side. Strong Stokes’ drifting velocity was predicted in the estuary, so that the Lagrangian trajectories of particles were characterized by strong nonlinear processes that differ significantly from those estimated by the Eulerian residual currents.

Energetic baroclinic super‐tidal oscillations on the southeast Florida shelf

Historical and recent data reveal a very energetic regime on the shelf off southeast Florida. In addition to spin off eddies, large‐amplitude tidal velocity fluctuations with amplitudes exceeding 0.5 ms−1 are observed. Recent exploratory measurements conducted as a part of the South Florida Ocean Measurement Center (SFOMC) show that the time scale of these oscillations is about 10 hrs. This period does not coincide either with the inertial period (27 Hrs) or with the semidiurnal M2 (12.42 hrs) or S2 (12 hrs) tidal constituents. In addition, these internal oscillations appear to be modulated seasonally. A possible explanation is that these oscillations are near‐resonant internal seiches generated by barotropic tidal wave in the channel between Florida and Bahamas.

M2 tidal dynamics in the Ross Sea

In certain regions of the Southern Ocean, tidal energy is believed to foster the mixing of different water masses, which eventually contribute to the formation of deep and bottom waters. The Ross Sea is one of the major ventilation sites of the global ocean abyss and a region of sparse tidal observations. We investigated M2 tidal dynamics in the Ross Sea using a three-dimensional sigma coordinate model, the Regional Ocean Model System (ROMS). Realistic topography and hydrography from existing observational data were used with a single tidal constituent, the semi-diurnal M2. The model fields faithfully reproduced the major features of the tidal circulation and had reasonable agreement with ten existing tidal elevation observations and forty-two existing tidal current measurements. The differences were attributed primarily to topographic errors. Internal tides were generated at the continental shelf/slope break and other areas of steep topography. Strong vertical shears in the horizontal velocities occurred under and at the edges of the Ross Ice Shelf and along the continental shelf/slope break. Estimates of lead formation based on divergence of baroclinic velocities were significantly higher than those based on barotrophic velocities, reaching over 10% at the continental shelf/slope break.

Tidal Mixing in the Southern Weddell Sea: Results from a Three-Dimensional Model

Abstract A three-dimensional primitive equation ocean model is used to study the magnitude and distribution of tidal mixing in the southern Weddell Sea. The contributions of (i) semidiurnal barotropic constituents M2 and S2, (ii) internal tides, and (iii) diurnal barotropic tides are considered. Computed elevation cotidal charts are generally consistent with our knowledge and observations for the region. The model reproduces maximum semidiurnal tidal elevations of about 1.6 m and 1.0 m for M2 and S2, respectively. An internal tide of moderate strength is generated over the slope, propagating in the alongslope direction but rapidly dissipating. On the continental shelf, a thick benthic boundary layer (150 m) develops due to the proximity of the critical latitude for the M2 constituent. Typical M2 and S2 baroclinic tidal currents at the shelf break are 7 and 4 cm s−1, respectively. In general, the tidal currents produce strong mixing in the bottom boundary layer at the shelf break and on the shelf leading t...

Vertical structure of turbulence on the southern flank of Georges Bank

Microstructure and acoustic Doppler current profiler measurements were taken at two sites on Georges Bank: in a shallow (45 m) well‐mixed region on top of the bank and in a deeper (75 m) more stratified region on the southern flank. Each site was visited twice, April 25 to May 3, 1995, and June 6–16, 1995. At both sites the dominant variability in the turbulent kinetic energy dissipation rate ε was related to the semidiurnal M2 tide. In the well‐mixed lower portions of the water column a phase delay was observed between ε and the current speed. The delay increased with height above the bottom. There was also a depth‐dependent phase delay in the square of the vertical shear of horizontal velocity, S2, of the M2 component. This phase lag has a depth dependence similar to that found for ε, which suggests that the turbulent mixing is locally generated by the current shear, as opposed to having propagated from the boundary.

Modeling Local Tidal Constituents Using TOPEX/POSEIDON SSH for the Malaysian Marine Region

A new Local Ocean Tide Model, has been produced for the Exclusive Economic Zone (EEZ) of Malaysia, which incorporates some of the latest TOPEX/POSEIDON data for the years 1992 to 1998. Local tide gauge data are used as a comparison, along with another leading Global Ocean Tide Model, Ori96. The leading diurnal and semidiurnal constituents M2, S2, N2, K1, O1, P1 and Q1 are reproduced using TOPEX/POSEIDON Sea Surface Heights (SSH) in a response analysis type least squares derivation following Munk and Cartwright (1966).

Observations of turbulence in a tidal beam and across a coastal ridge

During a microstructure survey off California in Monterey Bay, we found a midwater beam of strong turbulence emanating from the shelf break along the ray path of the semidiurnal M2 internal tide. Within the 50‐m‐thick beam the turbulence kinetic energy dissipation rate ε exceeded 10−6 W kg−1, and the diapycnal eddy diffusivity Kρ was >0.01 m2 s−1. The beam extended 4 km off the shelf break. Several factors suggest that this beam of strong turbulence resulted from the breaking of semidiurnal internal tides: the beam appeared to originate from the shelf break, which is a potential generation site for semidiurnal internal tides; the beam closely followed the ray path of the semidiurnal internal tide; the average ε off the shelf break varied by a factor of 100 with a semidiurnal tidal periodicity; the isopycnal displacement confirmed the presence of semidiurnal internal tides. Processes associated with the breaking of internal tides are intermittent and sporadic. At the same location we also observed equally intense turbulence in a ∼100‐m‐thick layer of stratified water across the ridge of a sea fan. This layer of strong turbulence was separated from the bottom and was clearly not generated by bottom friction. Although less well resolved in time, the strong turbulence above the bottom seemed to vary with the semidiurnal tide and existed at the lee of the ridge, where the isopycnal surface dipped and rebounded in a pattern resembling that of internal hydraulic jumps. On the basis of the behavior of the density field, we believe that the deep mixing was most likely produced by the across‐ridge current of internal tides. The breaking of internal tides at middepth, where the Richardson number is close to the critical value, is likely due to shear instability. The presence of the coastal ridge provides an alternative pathway for converting energy from internal tides to turbulence via internal hydraulics. Multiplying the average ε in the midwater beam by the length of the global coastline gives 31 GW, only a small fraction of the estimated 360 GW dissipated globally by M2 internal tides. Our observations suggest that either most internal tides are generated away from shelf breaks or most internal tides generated at shelf breaks propagate away from their generation sites, rather than dissipate locally, and eventually contribute to pelagic mixing.

The ocean tide gravimetric loading reconsidered

In 1994–95, a set of new global ocean tide models computed by different teams was made available to the scientific community. These models were derived from the analysis of satellite altimetric data, numerical hydrodynamics or a combination of both. The task is now to evaluate their relative accuracy, in particular with independent data. The data bank prepared by the International Center for Earth Tides (ICET, Melchior 1994) gives us a unique opportunity to compare the tidal models by testing their capability to predict the induced gravimetric loading effects. The more recent versions (released in 1995) of the models by Ma et al. (1994) and by Schrama and Ray (1994) both completed at high latitudes by the Le Provost et al. (1994) FES94.1 model have the best scores for the semidiurnal M2 wave, with a standard deviation (SD) of the gravimetric data residues less than 0.540 µgal. Schwiderski (1980) and Egbert et al. (1994) models give the smallest residual SD, about 0.370 µgal, for the diurnal O1 component. However, the ordering of the models may change when we focus on some particular regions of the globe.

Wassertransport und Wasseraustausch im nordfriesischen Wattenmeer — Ergebnisse numerischer Untersuchungen

A three-dimensional baroclinic circulation model and a Lagrangian dispersion model are presented which were used to compute water transports and mixing times in sub-areas of the North Frisian Wadden Sea. Both models were used to simulate tide-induced water motions forced by the principal lunar semidiurnal tide M2, and two selected periods taking into account current meteorological and thermodynamic conditions. Wind speeds were low during the simulation period in summer 1994, while gale-force winds prevailed during the winter 1994 simulation period. The circulation model was used for determining water transports across selected transects in the Wadden Sea. For sub-areas of the Wadden Sea, flushing times were computed on the basis of water transports and volumes of the sub-areas. For a first rough estimate, turnover times were derived from a fixed percentage of the tidal prism. More precise data for the turnover times were determined by means of the dispersion model. When comparing the mixing times computed by different methods, only partial correspondence was found. Parameterization of the turnover time by means of the tidal prism was found to produce some unrealistic results. The turnover times computed with the dispersion model for the summer period ranged between 1 and 7 tidal periods in most sub-areas of the North Frisian Wadden Sea. During the simulation period in winter, both water transports and turnover times deviated substantially from the data of the other case studies.

Ocean tides under the Filchner-Ronne Ice Shelf, Antarctica

A depth-averaged finite-difference numerical model has been used to make a preliminary study of the tides under the Filchner–Ronne Ice Shelf. Open boundary conditions were specified using the global ocean model of Schwiderski. Tidal constituents for the two principal semi-diurnal constituents M2 and S2, and the two principal diurnal constituents Ο1 and K1 were extracted from computed sea-surface elevations by harmonic analysis. Measured values near to the grounding line could only be reproduced satisfactorily by increasing the bottom friction coefficient under the ice to 50 times the open-ocean value. This destroys any agreement near the ice front or at pelagic sites. It is thought that a friction coefficient which varies with distance under the ice would be able to reproduce better all the available measurements. More tidal measurements are required to validate any model of the region with model experiments being used to help pinpoint possible sites for instrument deployment.

Ocean tides under the Filchner-Ronne Ice Shelf, Antarctica

A depth-averaged finite-difference numerical model has been used to make a preliminary study of the tides under the Filchner–Ronne Ice Shelf. Open boundary conditions were specified using the global ocean model of Schwiderski. Tidal constituents for the two principal semi-diurnal constituents M2 and S2, and the two principal diurnal constituents Ο1 and K1 were extracted from computed sea-surface elevations by harmonic analysis. Measured values near to the grounding line could only be reproduced satisfactorily by increasing the bottom friction coefficient under the ice to 50 times the open-ocean value. This destroys any agreement near the ice front or at pelagic sites. It is thought that a friction coefficient which varies with distance under the ice would be able to reproduce better all the available measurements. More tidal measurements are required to validate any model of the region with model experiments being used to help pinpoint possible sites for instrument deployment.

Flow through the Mernoo Saddle, New Zealand

Abstract Data were analysed from two current meters moored 100 and 300 m off the seabed in the Mernoo Saddle from June to November 1988. The flow was dominated by the lunar semidiurnal constituent M2 with an amplitude of 15.1 cm s−1 at the upper level and 15.8 cm s−1 at the lower level. The major axes of the tidal ellipses for the semidiurnal constituents were aligned more or less alongshore whereas those of the two largest diurnal constituents, Oj and Ki, were aligned across‐shore. Peak tidal period flows of 28 cm s−1 (upper) and 33 cm s−1 (lower) were recorded. Over the entire record, net flow was to the north at an average speed of 3.1 cm s−1 but there were periods of up to 5 weeks during which net flow was to the south. Strong southward flow events lasting 10–12 days were recorded on three occasions and the maximum current speed recorded was 67 cm s−1 to the south. Satellite imagery was used to show that these southward flow events coincide with the influx of warm water at the surface within 5 km of the coast near Kaikoura, and we suggest that the southward flows are caused by this influx of warm water which is carried by eddies from the south of the Wairarapa eddy to the area immediately north of the Mernoo Saddle. There is some indication that internal tides may be significant in this area but inertial currents were found to be weak.

Some results of heterogeneous data inversions for oceanic tides

Many different instruments directly or indirectly observe the oceanic tidal movements. Among them, we consider here the coastal tide gauge and deep‐sea pressure recorder which provide at least the principal spectral constituents of the tidal height, the gravimeter which indirectly observes the oceanic tides through the gravitational effect generated by the deformation of the solid Earth under the ocean tidal mass load, and the satellite altimeter which samples the tides in the time domain and over the nearly whole ocean. Our present paper deals with an empirical method for the recovery of the oceanic tides by inversion of heterogeneous data sets. The aim is to take advantage of the different kinds of information coming from the measurement instruments in order to complete more accurate empirical solutions. First, tide gauge and gravity loading data are separately and jointly inverted to provide global charts of the major semidiurnal M2 wave. The results prove that the tide gauge data have a major contribution in the tidal mapping but also suggest that the gravity loading data distort the information. This is certainly due to unmodelled geophysical phenomena and instrumental errors. Second, tide gauge and satellite altimeter data are considered in a separate and a joint inversion computation to provide tidal estimations along a predefined geographical line in the North Atlantic. The results are accurate enough to make provision for the boundary conditions of an hydrodynamical tidal model. As an intrinsic advantage of the inversion method, a posteriori standard deviations and error covariances for all the solutions displayed are provided and analyzed.

Tilt observations using borehole tiltmeters: 1. Analysis of tidal and secular tilt

We have designed a borehole tiltmeter using two horizontal pendulums which have periods of 1 s. We have installed the instruments at seven sites in Colorado and Wyoming to evaluate the secular tilt, the tides, and the coherence between nearby instruments. Using 28 days of data from Boulder, Colorado, the standard deviations of the tidal estimates are 5% for the semidiurnal component M2 and 9% for the diurnal component O1. The estimates agree with models that include the body tide, the ocean load, and the topographic correction to better than the estimated uncertainty. Tidal measurements at Erie, Colorado, have larger, possibly nonrandom variability that may be caused by a coupling between the tides and long‐period tilts. The coherence between nearby instruments is ≳0.5 for frequencies ranging from 0.5 to 2 cycles per day, but drops to a much smaller value outside of this range. The secular tilt rate is quite variable and ranges from 0.1 to 1 μrad/yr. Measurements at Erie, Colorado, and in Yellowstone National Park, Wyoming, exhibit an annual or biannual periodicity with an amplitude of about 1 μrad, which is consistent with a 1/f2 extrapolation of the diurnal noise power to longer periods.