Tidal Residuals Research Articles

Separation of residual ocean tide signals in a collinear analysis of Geosat altimetry

The effects of residual ocean tide signals on altimetric mesoscale variability estimates are analyzed in the north east Atlantic region using one year of Geosat Exact Repeat Mission data. The variability is evaluated along collinear tracks and covariance functions are determined. Initial results show that the average variability is about 10 cm. Variability values of 15–20 cm are found between Iceland and the Faeroe Islands and values up to 1/2 m are found near the coast of the UK. Then a procedure for estimation of ocean tide signals combined with the collinear analyses was tested. A separation of the estimated tide residuals associated with M2, S2, and N2 resulted in a significant reduction of the variability. The average variability decreased to 5 cm and the temporal correlations vanished. A reduction of the large variability values from 15–50 cm to 5–10 cm demonstrates that significant residual ocean tide signals can be estimated and removed efficiently in a collinear analysis of the mesoscale ocean variability.

The Rose Spit Eddy in Dixon Entrance: Evidence for its existence and underlying dynamics

Abstract The existence and dynamics of the so‐called “Rose Spit Eddy” in Dixon Entrance, British Columbia, are investigated by (i) analysing published observations of low‐frequency Eulerian and Lagrangian currents in the region; (ii) interpreting tidal residuals produced by the Hecate Model (a non‐rotating hydraulic model of Hecate Strait and Dixon Entrance); and (iii) running a barotropic, non‐linear numerical tidal model over simplified topography to investigate residuals produced over the Rose Spit sill. Observations have consistently revealed persistent basin‐wide, surface‐intensified cyclonic shears within central and eastern Dixon Entrance. The Hecate hydraulic tidal model also produced a tidal residual cyclonic gyre in central Dixon Entrance, but with velocities considerably larger than those observed. Barotropic numerical simulations of tidal streams flowing over a representation of the Rose Spit sill produced residual flows along the sill in reasonable agreement with observations and theory. A so...

On tidal gravity, heat flow and lateral heterogeneities

Abstract Correlations between residuals of tidal gravity and terrestrial heat flow have been used recently as evidence that the tidal gravity response of the Earth can be measurably perturbed by lateral heterogeneities in the upper crust. The gravity residuals in these correlations are from the data bank of the International Center of Earth Tides (ICET). We believe that these correlations are spurious and not the result of physical effects of heat flow on tidal gravity. This conclusion is based on several inconsistencies and contradictions we have found in the data, assuming the influence of a physical effect, together with a consideration of important sources of error. The uncertainties in instrumental calibrations and oceanic load corrections used in forming the tidal residuals are shown to be capable of producing residuals larger than the effects of heat flow implied by the correlation results. Also, theory predicts that lateral heterogeneities in the upper crust, of the extent and magnitude indicated by seismology, would not affect tidal gravity at the level of the residuals in the reported correlations. We show that observations in central Europe with accurately calibrated modern gravimeters, and with close attention paid to oceanic corrections, are in excellent agreement with present tidal theory and reveal no effects of heat flow on tidal gravity. These observations include data from a superconducting gravimeter located in a region of anomalously high heat flow near Strasbourg, France.

Review of the physical oceanography of the North Sea

After a general consideration of the physical factors that are of special interest to ecology, the typical character of the North Sea is discussed. The emphasis is on the processes that are responsible for the physical environment. The dominant feature is the tidal motion. This is not only a mechanism for vertical and horizontal mixing. The tidal residuals also contribute to a basic circulation pattern that together with the long-term net effects of the wind-driven circulation and the baroclinic effects results in an overall transport that determines the major features of the distribution of the water properties. Superimposed on this there are variations (mainly wind-induced) and regional differences in a wide range of time- and length-scales. Some typical features of both the southern and northern part of the North Sea are discussed. The review is concluded with a discussion on the long-term variations in the physical conditions of the North Sea. These are mainly to changes in temperature, salinity and sea-level.

A finite‐element tidal model for the southwest coast of Vancouver Island

Abstract A finite‐element, barotropic, tidal model is developed for the southwest coast of Vancouver Island. The model is run with 10 tidal constituents and the results are compared with Flather's (1988) finite‐difference model, and extensive tide‐gauge and current‐meter observations. Although sea‐level amplitudes and phases are reproduced, on average, to within 0.4 cm and 0.6° for each constituent, the model currents do not compare as favourably. Evidence is shown that these inaccuracies are due to baroclinic effects that cannot be reproduced with a barotropic model. Tidal residuals calculated by the model demonstrate the existence of eddies off the tip of Cape Flattery and around the commercial fishing grounds at Swiftsure and Amphitrite Banks.

Lorentz Invariance as a Dynamic Symmetry

If all the forces of nature can be reduced to those which follow from a linear combination of a scalar and vector potential, as in electrodynamics, Lorentz invariance can be derived as a dynamic symmetry. All that has to be done is to assume that there is an all pervading substratum or ether, transmitting those forces through space, and that all physical bodies actually observed are held together by those forces. Under this assumption bodies in absolute motion through the substratum suffer a true contraction equal to the Lorentz contraction, and as a result of this contraction clocks in absolute motion go slower by the same amount. The velocity of light appears then to be equal in all inertial reference systems, if Einstein’s clock synchronization convention by reflected light signals is used and which presupposes this result. The Lorentz contraction and time dilation measured on an object at rest relative to an observer who gained a velocity by an accelerated motion is there explained as an illusion caused by a true Lorentz contraction and time dilation of the observer. Both the special relativistic kinematic interpretation and this alternative dynamic interpretation give identical results only in the adiabatic limit where the accelerations are small, because if the Lorentz contraction is a real physical effect, it must take a finite time. However, to break the peculiar interaction symmetry with the ether, and which in the dynamic interpretation is the cause for the Lorentz invariance, the accelerated motions must involve rotation. Only then can non-adiabatic relativity-violating effects be observed and which would establish a preferred reference system at rest with the ether. Under most circumstances relativity-violating effects resulting from such a dynamic interpretation of special relativity would be very small and difficult to observe, a likely reason why they have evaded their detection in the past. For the rotating earth a residual sideral tide has been observed with a superconducting gravimeter, and which could be explained by an “ether wind” of about 300 km /sec at rest with the cosmic microwave background radiation. However, because of the observational uncertainties in measuring the terrestrial tides no definite conclusion can be drawn. A number of new experiments are therefore needed to decide the question regarding a possible weak violation of special relativity.

Global mesoscale variability from collinear tracks of SEASAT altimeter data

In 1978, during the last 25 days of the SEASAT mission, the satellite ground tracks repeated within 2.5 km every 3 days. This yielded eight to nine sets of global collinear altimeter data with a cross‐track grid spacing of approximately 900 km at the equator and 600 km at mid‐latitude. Because the geoid is time‐invariant, such observations can reveal sea surface height variability due to dynamic ocean phenomena. We have solved for variations due to deep‐ocean mesoscale features by eliminating the longer wavelength deviations. Modeled tidal heights were first subtracted from the altimeter data, and linear trends were then removed from collinear segments approximately 2000 km in length. This second step eliminates relative orbit error together with any residual tide model errors. The resulting sea height profiles have a precision of a few centimeters, and the global variability map constructed from these data reveals a strikingly realistic view of mesoscale energetics. Maximum values of 20–40 cm rms variability are generated by meanders and eddies of five major current systems: Gulf Stream, Kuroshio, Agulhas, Antarctic Circumpolar, and Falkland/Brazil confluence. Perhaps a more significant discovery was the dominance of exceedingly small variability over vast regions of the oceans; approximately 70% of all global values were less than 5 cm. This category included the eastern North Pacific, eastern South Pacific, and almost the entire South Atlantic where values as small as 1–2 cm were common. With such a low level of background noise, even some currents with relatively small sea height signatures could be detected. In both the Atlantic and the Pacific, for example, the North Equatorial Current systems were clearly expressed as zonal bands of higher variability.

Thermal response of the bottom pressure sensor off the coast of the Tokai District, Central Honshu and its application to oceanographic analysis.

Thermal response of the telemetry bottom pressure sensor 100 km off the south coast of the Tokai District, central Honshu, is analyzed. It is shown, through the analysis, that there appear comparatively large (approximately 0.1°C) short-period bottom temperature changes at the rate of once per several months even just above the seabed 2200 m deep. At these times, the tidal residuals of bottom pressure have a tendency to show characteristic short-term changes of durations of ten days or more and amplitude less than 10 cmH2O. It is possibly due to mesoscale ocean eddies. The bottom variations of this temperature and pressure are compared with the oceanographic conditions, especially with the route of the Kuroshio, and some qualitative correlation is observed among them. Thus, it could be concluded that the bottom pressure records are applicable as an indicator for oceanographic variations off the Tokai District.

Real-time observation of precursory crustal level change by use of bottom pressure.

Ocean-bottom pressure at a depth of 2, 200m has been observed on real-time at an observation point 40km northwest of the Nankai trough since August 1978. The pressure data show a linear drifting trend of nearly +6 cmH2O/year, which is considered to be an instrumental drift. Some fluctuations having a period longer than a week with amplitudes less than 10 cmH2O are also seen on the data recorded. These must be caused by the oceanographic variations associated with the meandering of the Kuroshio. A large crustal level change just prior to (several days to several hours) a great earthquake, if any, could be detected on real-time by use of the tidal residuals. The threshold of ±10 cmH2O is proposed here on the basis of a simulation for a year. The threshold can further be improved by possible suppression of thermally induced instrumental noise, more precise tidal analysis and correction of the oceanographic variations, although it is no easy matter to achieve these points. This threshold is comparable to that for the coastal differential tide observation between Tago and Omaezaki. It is expected that the bottom pressure observation will serve as one of the monitoring tools for an earthquake occurrence in the sea area.

On mass transports generated by tides and long waves

For small-amplitude barotropic wave motion in a shallow fluid, Moore (1970) found that the associated mean mass transport is geostrophic, but otherwise arbitrary in the absence of friction. We show how weak friction, or starting the motion from rest, determines the mass transport by restricting circulation around closed geostrophic (f/h) contours. The resulting transport is quadratic in oscillatory quantities and depends on the friction type, but not on its (weak) magnitude. Comparison is made with earlier results in particular geometries. A tendency for anticyclonic circulation around shallow regions is found, and extends to large-amplitude oscillations where particle excursions exceed the topographic length scale. We suggest that numerical schemes for calculating tidal residuals should conserve mass and vorticity.

Residual flows and elevations in the southern North Sea

The distribution of residual flow and the variation in mean sea level in the southern North Sea have been simulated by using a two-dimensional, vertically integrated, numerical model. The tidal residuals (i.e. the nonoscillatory tidal component) associated with the principal, M 2 , constituent were calculated from a fully nonlinear model and in specifying the boundary conditions for this model, the technique used by Proudman (1957) to accommodate residual terms was adopted. The residual flows computed for the M 2 constituent were found to account for approximately one half of the net computed residuals and the flow distribution produced by the model was shown to be in excellent agreement with both observations and previous calculations (Nihoul & Ronday 1975). A linearized model was used to simulate the effect of the major non-tidal forcing phenomena, namely wind, density and sea-surface gradients. The magnitudes of the friction coefficients in the linearized model were evaluated in terms of the M 2 tidal velocities. In simulating the response of the region to an imposed wind field, boundary conditions were calculated by reference to the method of characteristics. The relation, calculated from the model, relating the wind speed to the resulting flow and the elevation gradient in the Dover Strait, was found to be in close agreement with the corresponding relation deduced from observations by Bowden (1956). Similarly, the long-term variation in mean sea level due to wind forcing calculated by the model was found to be in good agreement with the variation computed from observations by Rossiter (1967). It was shown that, subject to the assumption of vertical homogeneity implicit in the model, the residual flows and elevations generated by horizontal density gradients were of only a minor significance. The net residuals were obtained by superimposing the separate components, namely those of tidal, wind and sea-surface gradient origin. The magnitude of the sea-surface gradient was determined by ensuring a best fit between the computed and recorded variations in mean sea level along the Continental coast. The difference in mean sea level between the Continental and English coasts was then calculated directly and was found to be in agreement with the earlier estimate by Cartwright & Crease (1963). In addition, the corresponding datum differences between the English and Continental levelling networks were computed and were found to be in good agreement with the value calculated by using the most recent British and French levellings of the tidal datums at Dover and Dunkirk. The magnitude of the net residual flow, computed in conjunction with these net sea-level gradients, was also in excellent agreement with the net residual derived from over 9 years of cross-Channel cable recordings (Alcock & Cartwright 1977). In addition, the net residual flow computed for wind-free conditions was in close agreement with the results from current meter recordings under similar conditions (Prandle & Harrison 1975). The distribution of this net residual flow was found to be consistent with previous observations and estimations based on ( a ) temperature and salinity distributions, ( b )current meter measurements, ( c ) sea-bed drifters, ( d )distribution of caesium 137, ( e ) movement of sand waves and ( f ) independent modelling studies. In conclusion, the results of this study provide a framework which both connects and relates the established studies of residuals in the Southern Bight. In addition, for the first time, a complete and comprehensive description is presented of the contribution of each of the major residual forcing phenomena.

A Statistical Analysis of Storm Surges in Torres Strait

Tidal harmonic constituents were obtained from analysis of one year of simultaneous sea level observations at each of six stations in Torres Strait and the subsequent tidal residuals were computed. Examination of the residuals showed that Frederick Point and Twin Island have similar responses to meteorological effects; likewise Booby Island, Goods Island and Turtle Head have common characteristics. It was found that the east-west component of surface winds is mainly responsible for the generation and propagation of surges, and winds of velocity less than 12 m/s are insignificant in the generation of surges. Winds from the west develop positive surges west of Ince Point and negative surges east of Ince Point. The reverse is true for winds from the east. A regression technique was used to develop a system for forecasting surges using meteorological data available from nearby meteorological stations. Variations in mean sea level with periods of 3-4 days were observed. These oscillations were not simply related to any local meteorological effects and are considered to have their origin either in the Indian Ocean or in the Coral Sea. It is suggested that a mechanism exists whereby surges generated outside Torres Strait may affect surge levels within the Strait.

Tidal residuals in the English Channel

The amplitude and phase of tidal characteristics in the English Channel have been described both using numerical models (Grijalva, 1962; Hyacinthe & Kravtchenko, 1967) and a hydraulic model on a rotating table (Chabert d'Hières & le Provost, 1970). The aim behind the development of the numerical model described here is first to derive an accurate representation of the principal lunar semi-diurnal (M2) tide in the English Channel and then to use the currents generated by the tidal input to determine the tidal circulation patterns and residual flow through the English Channel. A test of the model must be its ability to reproduce the known clockwise eddy in Lyme Bay and the south-ward flow either side of Portland Bill. If these known tidal residuals can be reproduced then the model may help to elucidate residuals in other regions where the flow is unknown. In addition to deriving the mean tidal velocities, horizontal distributions for the mean squared and cubed values are calculated and the importance of these distributions in determining the nature of the bottom and the degree of stratification of the water column in summer is demonstrated.