Tidal Ellipse Parameters Research Articles

A note on interpreting tidal harmonic constants

The amplitudes and phase lags of tides or tidal currents, which are collectively known as tidal harmonic constants (THCs), cannot be interpolated linearly and separately. Mistreatment for the interpolations could occur, and indeed, it is seen even in the literature. This note clarifies this topic by providing correct formulas to interpret THCs. One has to perform a nonlinear and coupled interpolation of THCs to have equivalence to the liner interpolation in the time domain.Similarly, tidal current ellipse parameters (ep-parameters) cannot be interpolated linearly and separately. To interpolate ep-parameters, this note recommends that one should first convert them to amplitude and phase lag parameters (ap-parameters) and then use the nonlinear and coupled interpolants proposed herein to interpolate the ap-parameters, followed by converting the results back to ep-parameters.Examples are provided to illustrate the problems and MATLAB functions are provided in Appendix as interpolating tools.

An exploratory study of the variability of currents and density in the Marsdiep

Observational data of tidal currents and vertical stratification in a periodically-stratified estuarine basin are presented in this study. The data were collected between 2010 and 2012 during multiple surveys in the Marsdiep basin, which is part of the Western Dutch Wadden Sea. The aim of this study is to better understand the spatial variability of the tidal currents and the occurrence of vertical stratification in the Marsdiep basin. A harmonic analysis is applied to the depth-averaged velocity to obtain estimates of the tidal ellipse parameters of the M2 tidal constituent along the surveys. The spatial variation in magnitude of the tidal currents is complex but seems mainly related to water depth. This relationship varies in time on a daily to fortnightly timescale, which results in a variation of the lateral velocity shears over time. Furthermore, the tidally-averaged lateral density gradient is of the same order of magnitude as the longitudinal density gradient, which implies that cross-stream processes are important in the Marsdiep basin. At some locations, vertical stratification is only observed during the flood phase which seems mainly driven by lateral processes. This pattern is inconsistent with the classical alongstream tidal straining mechanism, where vertical stratification develops during ebb and diminishes during flood. It is hypothesized that vertical stratification during flood increases from neap to spring tidal conditions due to increased differential advection. The strength and timing of vertical stratification is shown to be highly spatially variable in the Marsdiep basin, which might have implications for the residual circulation patterns.

Skill testing a three‐dimensional global tide model to historical current meter records

We apply several skill tests to assess tidal currents within a three‐dimensional, eddy resolving, global ocean circulation model compared to over 5000 observational velocity records spanning 40 years. We examine the skill of the HYbrid Coordinate Ocean Model (HYCOM) on a regional, basin, and global scale and in deep versus shallow water. On a global scale, we examine the model tidal kinetic energy (KE) compared to the tidal KE estimated from the observational velocity records. We examine the vertical structure of the model tidal KE by averaging over predetermined depth bins. We also investigate the ability of the model to satisfy the 95% confidence intervals of the individual tidal ellipse parameters. On a basin scale, we determine if any bias exists in model performance with regards to a particular part of the global ocean and further investigate if any variability of model skill exists within the ocean basins by testing the model against smaller subsets of the observations. Our results show that the skill of the nondata assimilative HYCOM is comparable to the skill of the altimetric‐constrained model TPXO7.2. HYCOM is shown to have up to 20% higher skill in resolving the Greenwich phase of the tides on a global basis and demonstrates moderate skill in replicating the vertical structure of the tidal currents as represented by the current meters. HYCOM demonstrates up to 20% higher skill than TPXO7.2 for some ocean basins and some ocean regions but exhibits up to 20% weaker skill in the Southern Ocean.

Skill tests of three‐dimensional tidal currents in a global ocean model: A look at the North Atlantic

We present and apply several skill tests to assess tidal currents generated within a global ocean model compared to an archive of current meter records spanning 40 years. Within the North Atlantic we have identified over 1800 velocity records available for comparison to model output. The skill tests identify those regions where tidal ellipse parameters (semi‐major/minor axis, inclination and Greenwich phase) fall within 95% confidence intervals derived from observations. Additional skill tests examine the vertical and horizontal structure of the tidal currents using the correlation and root mean square error between the observations and model. The skill tests account for grid misrepresentation within the model by comparing model values in a local 9‐point neighborhood. Both the three‐dimensional structure of model tidal currents and barotropic model tidal currents are compared to the altimetry based barotropic model TPXO 7.2. Our results indicate that the non‐data assimilative ocean model performance is comparable to TPXO 7.2. The semi‐major axes of the semi‐diurnal constituents lie within the 95% confidence intervals between 40% and 60% of the time in some regions of the North Atlantic. The performance degrades when all tidal ellipse parameters are considered. Root mean square errors between the model and observations distributed through the water column are generally less than 1 cm s−1 representing an error of less than ∼10% for constituent M2. The model tides also exhibit high correlation with observations in the horizontal planes. The skill tests could be adapted to other sets of observations and other models.

Assessing the fidelity of surface currents from a coastal ocean model and HF radar using drifting buoys in the Middle Atlantic Bight

The rapid expansion of urbanization along the world’s coastal areas requires a more comprehensive and accurate understanding of the coastal ocean. Over the past several decades, numerical ocean circulation models have tried to provide such insight, based on our developing understanding of physical ocean processes. The systematic establishment of coastal ocean observation systems adopting cutting-edge technology, such as high frequency (HF) radar, satellite sensing, and gliders, has put such ocean model predictions to the test, by providing comprehensive observational datasets for the validation of numerical model forecasts. The New York Harbor Observing and Prediction System (NYHOPS) is a comprehensive system for understanding coastal ocean processes on the continental shelf waters of New York and New Jersey. To increase confidence in the system’s ocean circulation predictions in that area, a detailed validation exercise was carried out using HF radar and Lagrangian drifter-derived surface currents from three drifters obtained between March and October 2010. During that period, the root mean square (RMS) differences of both the east–west and north–south currents between NYHOPS and HF radar were approximately 15 cm s−1. Harmonic analysis of NYHOPS and HF radar surface currents shows similar tidal ellipse parameters for the dominant M2 tide, with a mean difference of 2.4 cm s−1 in the semi-major axis and 1.4 cm s−1 in the semi-minor axis and 3° in orientation and 10° in phase. Surface currents derived independently from drifters along their trajectories showed that NYHOPS and HF radar yielded similarly accurate results. RMS errors when compared to currents derived along the trajectory of the three drifters were approximately 10 cm s−1. Overall, the analysis suggests that NYHOPS and HF radar had similar skill in estimating the currents over the continental shelf waters of the Middle Atlantic Bight during this time period. An ensemble-based set of particle tracking simulations using one drifter which was tracked for 11 days showed that the ensemble mean separation generally increases with time in a linear fashion. The separation distance is not dominated by high frequency or short spatial scale wavelengths suggesting that both the NYHOPS and HF radar currents are representing tidal and inertial time scales correctly and resolving some of the smaller scale eddies. The growing ensemble mean separation distance is dominated by errors in the mean flow causing the drifters to slowly diverge from their observed positions. The separation distance for both HF radar and NYHOPS stays below 30 km after 5 days, and the two technologies have similar tracking skill at the 95 % level. For comparison, the ensemble mean distance of a drifter from its initial release location (persistence assumption) is estimated to be greater than 70 km in 5 days.

Tidal and wind-driven surface currents in the German Bight: HFR observations versus model simulations

Tidal and wind-driven surface currents in the German Bight between shallow mudflats of the North Frisian islands and the island of Helgoland are studied using coastal high-frequency radar (HFR) observations and hindcasts from a primitive equation numerical model. The setup of the observational system is described, and estimates of expected measurement errors are given. A quantitative comparison of numerical model results and observations is performed. The dominant tidal components are extracted from the two data sources using tidal harmonic analysis and the corresponding tidal ellipses are defined. Results show that the spatial patterns of different tidal ellipse parameters are consistent in the two data sets. Model sensitivity studies with constant and variable salinity and temperature distributions are used to study density-related mechanisms of circulation. Furthermore, the role of the surface wind field in driving the German Bight circulation is investigated using the complex correlation between wind and surface current vectors. The observed change of the respective correlation patterns from the coastal to open ocean is shown to be due to a combination of density effects, the coastline and topography. The overall conclusion is that HFR observations resolve the small-scale and rapidly evolving characteristics of coastal currents well in the studied area and could present an important component for regional operational oceanography when combined with numerical modelling. Some unresolved issues associated with the complex circulation and large instability of circulation in front of the Elbe River Estuary justify further considerations of this area using dedicated surveys and modelling efforts.

Numerical modeling of tide and tidal current in the kangjin bay, south sea, Korea

This study is based on a series of numerical modeling experiments to understand the tidal circulation in the Kangjin Bay (KB). The tidal circulation in the KB is mostly controlled by the inflow from two channels, Noryang and Daebang which introduce the open ocean water into the northern part of the KB with relatively strong tidal current, while in the southern part of the KB, shallowest region of the entire study area, weak tidal current prevails. The model prediction of the sea level agrees with observed records at skill scores exceeding 90 % in terms of the four major tidal constituents (M2, S2, K1, O1). However, the skill scores for the tidal current show relatively lower values of 87, 99, 59, 23 for the semi-major axes of the constituents, respectively. The tidal ellipse parameters in the KB are such that the semi-major axes of the ellipse for M2 range from 1.7 to 38.5 cm/s and those for S2 range from 0.5 to 14.4 cm/s. The orientations of the major-axes show parallel with the local isobath. The eccentricity values at various grid points of ellipses for M2 and S2 are very low with 0.2 and 0.06 on the average, respectively illustrating that the tidal current in the KB is strongly recti-linear. The magnitude of the tidal residual current speed in the KB is on the order of a few cm/s and its distribution pattern is very complex. One of the most prominent features is found to be the counter-clockwise eddy recirculation cell at the mouth of the Daebang Channel.

The structure of tides in the Western Iberian region

A s-coordinate three-dimensional model, regional ocean modeling system (ROMS), was implemented in the Western Iberian region ranging from the coast to 11°W aiming high-resolution tidal simulations for an homogeneous ocean. The features for tidal heights and ellipses for the principal constituents, M 2, S 2, N 2, K 2, K 1, O 1, P 1 and Q 1, were imposed at the boundaries of the model. A tidal analysis for heights and tidal currents was done allowing to calculate two-dimensional distribution of amplitudes and three-dimensional structure of tidal currents. The amplitudes and phases for heights agree with previous results and observations, showing a good precision on the tidal propagation in the interior of the domain. Tidal kinetic energy is dominated by the semi-diurnal components, mainly M 2, and increases on the shelf. Over the Lisbon Promontory the diurnal component K 1 is however the second more energetic harmonic. Vertical variation of tidal ellipse parameters evidences the different structure of semi-diurnal and diurnal tidal components, as well as differences between the open sea and shelf tidal circulation.

A 3D boundary-fitted barotropic hydrodynamic model for the New York Harbor region

A three-dimensional barotropic hydrodynamic model application to the New York Harbor Region is performed using the Boundary-Fitted HYDROdynamic model (BFHYDRO). The model forcing functions consist of surface elevations along the open boundaries, hourly winds, and fresh water flows from the rivers and sewage flows. A comprehensive skill assessment of the model predictions is done using observed surface elevations and three-dimensional currents. The model-predicted surface elevations compare well with the observed surface elevations at four stations. Mean errors in the model-predicted surface elevations are less than 4% and correlation coefficients exceed 0.985. Model-predicted three-dimensional currents at Verrazano Narrows show excellent comparison with the observations, with mean errors less than 11% and correlation coefficients exceeding 0.960. Model-predicted three-dimensional currents at Bergen Point compare well with the observations, with mean errors less than 15% and correlation coefficients exceeding 0.897. The surface elevation amplitudes and phases of the principal tidal constituents at nine tidal stations, obtained from a harmonic analysis of a 60-day simulation compare well with the observed data. The predicted amplitude and phase of the M 2 tidal constituent at these stations are, respectively, within 5 cm and 6° of the observed data. The model-predicted tidal ellipse parameters for the major tidal constituents compare well with the observations at Verrazano Narrows and Bergen Point. The model-predicted along channel sub-tidal currents also compare well with the observations. The semi-diurnal tidal ranges and spring and neap tidal cycles of the surface elevations and currents are well reproduced in the model at all stations. The observed currents at Bergen Point were shown to be flood dominant through tidal distortion analysis. The model-predicted currents also showed Newark Bay and Arthur Kill to be flood dominant systems. The model predictions showed the occurrence of a pronounced flow separation and formation of a pair of counter-rotating eddies in the Lower New York Bay. The model-predicted residual circulation pattern showed many gyres in the Harbor Region and Jamaica Bay.

Tidal currents in the St. Lawrence Island region

Vertical and spatial variability of tidal currents in the northern part of the Bering Sea near St. Lawrence Island were examined using observations made at 17 new and historical current meter mooring locations. The semidiurnal currents dominate over the diurnal currents. Semidiurnal currents exhibit a seasonal modulation with currents being somewhat stronger during the summer and fall when the density structure displays two‐layer stratification. Diurnal currents exhibit a weak semiannual modulation. Examination of the vertical structure of tidal currents shows that maximum semidiurnal currents are observed in the upper or middle layers down to a depth of about 20 m, and below this depth the energy of the semidiurnal currents decreases rapidly. However, the energy of diurnal band currents remains almost constant with depth, decreasing only in close proximity to the bottom. Rotary spectral analysis applied to the records shows further differences: the M2 clockwise (CW) component of rotation dominates in the upper and middle water column but the counterclockwise component (CCW) dominates near the bottom. Interpretation of these observed results points to the different bottom boundary layers (BBL) for the CW and CCW motions in addition to the role of density stratification in organizing the BBL. We compare results of a vertically averaged two‐dimensional model to the observationally derived tidal ellipse parameters and show that the barotropic formulation provides a first‐order description of the tidal regime within the domain.

Observed and modelled tidal currents in the New Zealand region

Tidal currents derived from current meter measurements are compared with the output from a barotropic tidal model of the New Zealand region. For the semi‐diurnal constituents there was very good agreement for the M2 tide and good agreement for the S2 tide. For the diurnal constituents (Kl, Ol) it was found that as the amplitude of the constituents decreased so did both the model/observation agreement and the accuracy of the observed tidal ellipse parameters. Consequently it was not possible to decide whether differences arose through shortcomings in the model or in the data. However, the overall performance of the model as a prognostic tool for ocean tidal current simulation appears to be good.

Acoustic Doppler Current Profiler measurements of the semi‐diurnal internal tide on the west coast of New Zealand

Abstract Current measurements made by an Acoustic Doppler Current Profiler detail the vertical structure of the internal tide for a site at the continental shelf break on the west coast of New Zealand. The measurements, made over 10 h in late winter, had an 8 m vertical resolution. Tidal analysis of the velocity data shows a 60° change in tidal phase and a 90° change in tide ellipse orientation across the base of the mixed layer. The profiles of tidal ellipse parameters are shown to be consistent with the sum of a barotropic tide and an internal tide in a two density‐layer ocean. The barotropic tidal amplitude was 10 cm s−1 whereas the internal tide had a 6.3 cm s−1 amplitude. Both the barotropic and internal modes propagate in a direction approximately normal to the topography.

Tidal current fluctuations in the Soya Current

Long-term current measurements were carried out near the Soya Strait in the Okhotsk Sea during a period from February 1980 to September 1982. The data were divided into five segments, each being 150 days long, and the tidal ellipse parameters of major axis, minor axis, orientation, and phase for the four major constituents (M2, S2, K1 and O1 tides) were calculated at each segment. The major axis of the mean tidal ellipse averaged over five segments was 29.9 cm sec−1 for O1 tide, 28.3 cm sec−1 for K1 tide, 10.4 cm sec−1 for M2 tide, and 3.7 cm sec−1 for S2 tide. The phase and orientation of the tidal ellipse were much stable. But, the root mean square deviations of the major axis reached 20% of the mean values for all four constituents. The tidal currents estimated from the sea level records at Wakkanai and Esashi along the Hokkaido coast in the Okhotsk Sea show that their amplitudes and phases are in good agreement with the observed ones for all four constituents.