Internal tides and waves near the continental shelf edge

Abstract

The subject is reviewed from the viewpoints of theory, internal tide and wave structure and their implications.

A wider theoretical context suggests scope for further investigation of natural or nearly-trapped forms above the inertial frequency.

Although internal tides in many locations are observed to have first-mode vertical structure, higher modes are seen offshore from shallow shelf-break forcing and for particular Froude numbers, and may be expected locally near generation. Bottom intensification is often observed where the sea floor matches the characteristic slope. Solitons form from internal tides of large amplitude or at large changes of depth.

Internal tides and solitons are observed also at many sills and in straits, and to intensify in canyons.

Non-linear effects of the waves, especially solitons, include the conveyance of water, nutrients, ‘‘mixing potential'’ etc. away from their source to other locations, and the generation of mean currents. The waves transfer energy and possibly heat between the ocean and shelf, may be a source of medium frequency waves on the shelf (periods of minutes) and can contribute to interior mixing and overturning, bottom stirring and sediment movement.     

Geodetic observation of sea-level change and crustal deformation in the Baltic Sea region

Based on tide gauge observations spanning almost 200 years, homogeneous time series of the mean relative sea level were derived for nine sites at the southern coast of the Baltic Sea. Our regionally concentrated data were complemented by long-term relative sea-level records retrieved from the data base of the Permanent Service for Mean Sea Level (PSMSL). From these records relative sea-level change rates were derived at 51 tide gauge stations for the period between 1908 and 2007. A minimum observation time of 60 years is required for the determination of reliable sea-level rates. At present, no anthropogenic acceleration in sea-level rise is detected in the tide gauge observations in the southern Baltic. The spatial variation of the relative sea-level rates reflects the fingerprint of GIA-induced crustal uplift. Time series of extreme sea levels were also inferred from the tide gauge records. They were complemented by water level information from historic storm surge marks preserved along the German Baltic coast. Based on this combined dataset the incidence and spatial variation of extreme sea levels induced by storm surges were analysed yielding important information for hazard assessments. Permanent GPS observations were used to determine recent crustal deformation rates for 44 stations in the Baltic Sea region. The GPS derived height change rates were applied to reduce the relative sea-level changes observed by tide gauges yielding an estimate for the eustatic sea-level change. For 13 tide gauge-GPS colocation sites a mean eustatic sea-level trend of 1.3 mm/a was derived for the last 100 years.     

Vertical crustal motions from differential tide gauge observations and satellite altimetry in southern Italy

Our goal is to determine vertical crustal movement rates from tide gauge and satellite altimetry measurements. Tide gauges measure sea level, but as they are fixed to the crust, they sense both sea surface height variations and vertical crustal movements. The differential sea level rates of sufficiently nearby stations are a good means to determine differential crustal movement rates, when sea level height variations can be assumed to be homogeneous. Satellite altimetric measurements determine sea surface height variations directly and can be used to separate the crustal signal from the sea surface height variations in tide gauge measurements. The correction of the tide gauge sea level rates for the sea surface height contribution requires collocation of the satellite pass and the tide gauge station. We show that even if this is not the case, the satellite altimetric observations enable correction of differential tide gauge rates for the effects of sea surface rate inhomogeneities.     

Experimental estimate of a relation between sea wave energies and the Earth’s crust microdeformations

The experimental data in the microseismic frequency range obtained using the seismo-acoustic-hydrophysical measurement complex are analyzed. The emphasis is put on estimating the ratio between the energy of surface sea wind waves in the area of the Japan Sea where the complex was located and the Earth’s crust microdeformations in this frequency range. The experimental evaluate obtained allow us to estimate the energy re-distribution at the hydrosphere-lithosphere boundary.     

Long period edge waves off Southern Africa

Long gravity wave height oscillations of up to 60 cm with periods between 12 min and 1 h have been observed on tide gauge recordings from the southern coast of South Africa. Short period (30 min to 1 h), small height (3 mb) air pressure pulses were recorded at stations along the same coastline. Two separate events of contrasting nature are described in detail. The simple model of Snodgrass et al. (1962, Journal of Marine Research, 20, 3–30) is used to explain the sea waves as resonant, coastally trapped, edge waves on the Agulhas Bank forced by the atmospheric pulses.     

集成奇异谱分析和自回归滑动平均预测日本近海海平面变化

本文从日本沿岸选取了28个验潮站及联测的GPS站,利用奇异谱分析（Singular Spectrum Analysis,SSA）和SSA+自回归滑动平均（Auto Regression Moving Average,ARMA）方法预测了2014—2018年的近海海平面变化和地壳垂直变化.并用同时段的验潮及GPS的实际测量值进行验证,结果显示,SSA+ARMA预测的相对海平面精度为0.0357~0.0607 m,地壳垂直运动的精度为0.0049~0.0077 m,绝对海平面的精度为0.0433~0.0683 m,且三者SSA+ARMA的预测结果均优于只用SSA预测的结果.在此基础上本文利用SSA+ARMA预测了日本沿岸2019—2023年的近海绝对海平面变化,结果显示,2019—2023年的平均海面高较往年（2014—2018）升高0.0353 m,2003—2023年绝对海平面的变化率为0.0039 m·a^-1,预测结果较为理想.     

Influence of tide and waves on water renewal in Óbidos Lagoon, Portugal

The role of oceanic tide, wind stress, freshwater river inflows, and waves in the long-term circulation and residence time in óbidos Lagoon is investigated using a sensitivity analysis carried out by means of a two-dimensional model. MOHID modeling system coupled to Steady-State Spectral Wave model for simulate óbidos Lagoon circulation were implemented. For residence time calculus, a Lagrangian transport model was used. Tidal forcing is shown to be the dominant forcing, although storm waves must be considered to simulate accurately the long-term circulation. Tidal forcing enhances a spatial distribution in water residence time. Renewal time scales varies from values of 2 days in the near-ocean areas and 3 weeks in the inner areas. Freshwater river inflows decrease the residence time, while waves increase. In heavy rain periods, the water residence time decreases by about 40% in the upper lagoon. When wave forcing is considered, the residence time increases between 10% and 50% depending on lagoon area. The increase in residence time is explained by the sea level rise within lagoon (~1 m above average lagoon sea level) during storm wave periods. Average residence time is 16 days for tidal forcing, 9 days when the rivers are included (wet period), and 18 days when the waves are considered.     

Correcting High-Resolution Borehole Strainmeter Data from Complex External Influences and Partial-Solid Coupling: the Case of Trizonia,Rift of Corinth (Greece)

High-resolution borehole strainmeters are usually installed in tectonically active regions in order to detect slow-slip events, and to estimate slow transients related to earthquake swarms. However, they are also sensitive to other numerous influences, internal or external. Furthermore, the quality of their coupling to the rock through cementation, and the mechanical properties of the rock mass around them, have a critical influence on their records. Many of the existing strainmeters present such problems, and the correction for these effects often remains a challenge. In this paper, we present the analysis of the records of a high-resolution borehole dilatometer (Sacks–Evertson), located in the seismically active rift of Corinth (Greece) (station TRZ in the Trizonia island). We show that the instrument suffers from an only partial-solid coupling, and that the nearby sea tides have a direct (through elastic response) and indirect (through pore-pressure diffusion) effect on the dilatation signal, which adds up to the solid tidal strain source. We propose a methodology that allows, in a first step, to better separate the internal (solid tide) from the external (air pressure, sea level) influences, by calculating a frequency-dependent transfer function outside the range of the tidal periods. We then extrapolate this function, in particular at the tidal periods. In a second step, the resulting variation with frequency of the coupling coefficients with sea level led us to estimate the proportion of instrument not solidly cemented to rock (thus in contact with water pore pressure), which is about 90 % of the total height. Despite the small proportion of solid coupling, the sensor resolution remains very good up to a few tens of hours of a time period, thanks to the confining effects of the rocks on the local pore pressure. These results allow us to correct for the external effects, and reduce the associated variance by 80–90 % (in the period range of minutes to days). The empirical correction of the sea level effect could be explained using a simple Boussinesq’s approximation and 1D pore-pressure diffusion model, which contributed to better constraint of some of the poro-elastic parameters in the vicinity of the instrument. After correction, the solid tidal signal at the 24-h period is almost anti-correlated with those of the theoretical solid tide. This surprising result is consistent with a similar anti-correlation observed for the longest period surface waves (200 s) comparing the TRZ dilatometer signals to the strain measured by a nearby borehole strainmeter (MOK, 15 km). This could be related to the presence of a shallow fault close to the instrument, which would creep in response to seismic wave-related stress.     

Remote and local forcing of a coastal lagoon: The Virginia Coast Reserve

The effects of local and remote wind forcing of water level heights in the Virginia Coast Reserve (VCR) are examined in order to determine the significant forces governing estuarine motions over subtidal time scales. Recent (1996–2008) data from tide and wind stations in the lagoon, a tide station to the north at Sandy Hook, NJ, and one offshore wind station at the Chesapeake Light Tower are examined. Sea surface height spectrum calculations reveal significant diurnal and semidiurnal tidal effects along with subtidal variations, but a suppressed inertial signal. Sea-surface heights (SSH) with 2–5 day periods at Wachapreague, VA are coherent with those at Sandy Hook and lag them in time, suggesting that southward-propagating continental shelf waves provide subtidal variability within the lagoon. The coherence between lagoon winds and sea surface height, as well as between winds and cross-lagoon sea height gradient, were significant at a relatively small number of frequency and wind direction combinations. The frequencies at which this wind forcing occurs are the tidal and subtidal bands present to the north, so that lagoon winds selectively augment existing SSH signals, but do not generate them. The impact of the wind direction is closely related to the geometry of the lagoon and bounding landmasses. The effect of wind stress is also constrained by geometry in affecting the cross-lagoon water height gradient. Water levels at subtidal frequencies are likely forced by a combination of local wind forcing, remote wind forcing and oceanic forcing modified by the complex topography of the lagoon, shelf, and barrier islands.     

Ionospheric effects of Poincaré waves in the observations of the total electron content

Disturbances of the daily variations in the total electron content (TEC) of the ionosphere during and after geomagnetic storms, obtained from the observations of the GPS satellite signals, are considered. The specific features of these disturbances consist in the intensification of the variations with periods of 4–6 h, the amplitude of which increase at midlatitudes, and in a weak dependence of local maximums on latitude and their considerable longitudinal variability. The possibility of explaining observed disturbances of the considered daily variations by the generation of standing planetary Poincaré waves is discussed. The estimated periods of Poincaré waves, latitudinal structure of these waves, and their ionospheric effects make it possible to qualitatively explain the observed specific variations in TEC.     

Fortnightly oscillations observed in the Adriatic Sea

This paper documents the occurrence of strong fortnightly oscillations in the Adriatic Sea frequently observed in the current measurements. For that purpose, we analyzed half-decadal sea level series and long-term currents collected within different parts and layers of the Adriatic Sea. Harmonic analysis and band-pass filter with cutoff periods at 10 and 20 days have been applied to the series. The sea level Mf tide is found to be the only significant tidal constituent over periods between the diurnal and semi-annual ones, having no significant phase variations in the Adriatic Sea. Moreover, the currents on periods between 10 and 20 days could only partially be explained by atmospheric forcing. The fact that they are in-phase with the Mf tide gives a hint on a possible mechanism responsible for the generation of these oscillations. Additionally, these currents are usually strongly amplified during a weakly stratified season, indicating a baroclinic mechanism responsible for the multiplication of the fortnightly currents.     

强震前海平面异常变化特征研究

使用渤海沿岸8个验潮站的海潮潮位观测资料,根据近海或沿岸地区强震前后海平面变化的实例,分析了海平面变化的前兆意义。资料证实,大部分近海大地震前局部海域存在着可以识别的海平面异常变化。通过周期分析方法和潮汐分析方法来消除各种周期及非周期因素的影响,可以显示出地壳垂直形变的变化,分析结果表明,渤海沿岸的海平面变化不仅具有丰富的地质构造活动信息,而且可能反映较大地震前后的地壳形变过程。提取海平面地壳垂直形变信息对较大地震的预报和与海洋有关灾害的预测有重要意义。     

The effect of the Baltic Sea level on gravity at the Metsähovi station

The loading effect of the Baltic Sea is immediately recognizable in the gravity record of the superconducting gravimeter T020 in Metsähovi, Finland, by simply inspecting residual gravity together with the tide gauge record at Helsinki 30 km away. The station is 10 km from the nearest bay of the Baltic Sea and 15 km from the open sea. Sea level variations in the Baltic are non-tidal and driven at short periods primarily by wind stress, at longer periods by water exchange through the Danish straits. Locally they can have a range of 2–3 m. Loading calculations show that a uniform layer of water covering the complete Baltic Sea increases the gravity in Metsähovi by 31 nm/s² per 1 m of water, and the vertical deformation is −11 mm. The observed gravity response to the local sea level is generally less, since the variations at short periods are far from uniform areally, the same water volume just being redistributed to different places. Regression of the whole gravity record (1994-2001) on local sea level gives 50–70% of the uniform layer response, as do loading calculations using actual water distributions derived from 11 tide gauges. However, both fits are dominated by some extreme values of short duration, and parts of the gravity record with long-period variations in sea level are close to the uniform layer response. The gravity observations can be used to test corrections for other co-located geodetic observations (GPS, satellite laser ranging) which are influenced by the load effect but not sensitive enough to discriminate between models.     

High-frequency internal wave motions at the ANTARES site in the deep Western Mediterranean

High-frequency internal wave motions of periods down to 20 min have been observed in a yearlong record from the deep Western Mediterranean, mainly in vertical currents. The observations were made using the ANTARES neutrino telescope infrastructure. One line of the telescope is instrumented with environmental monitoring devices, and in particular with an Acoustic Doppler Current Profiler that was used to measure currents around 2,200 m. Such high-frequency internal waves are commonly observed much closer to the sea surface where the vertical density stratification is more stable than in the deep sea. In this paper, they are supported by the relatively large stratification following newly formed dense water. During the severe winters of 2005 and 2006, deep dense-water formation occurred in the Ligurian subbasin. Its collapse and spread over the sea floor across the basin remained detectable for at least 3 years as deduced from the present yearlong current record, which is from 2008. The observed high-frequency internal waves match the occasional density stratification observed in ～1-m-thin layers using previous shipborne conductivity–temperature–depth measurements. Such layers and waves are relatively unusual in the deep Mediterranean, where commonly several hundreds-of-meters-thick near-homogeneous layers dominate. Such thick near-homogeneous layers provide about a half-decade narrow internal wave band around the inertial frequency (f). In contrast, the presently observed vertical currents occasionally show a “small-scale” internal wave band that is on average 1.5 decades wide, associated with thin-layer stratification. In spite of its relatively large width, this band still shows variance peaking near f rather than near the large-scale buoyancy frequency N (= 2.3–4.5f) and this variance is found to increase with increasing N.     

A comment on the use of spectral characteristics of teleseismic body waves to evaluate fine crustal structure

An investigation of the crustal response in the time and frequency domains is presented to show that for models with similar crustal transit times of P and S waves, any important changes in the internal configuration of the crust such as layering, layer thickness and velocity contrast only influence the amplitudes of the transfer function ratio. Frequency positions of peaks and troughs remain unperturbed unless the total transit time of P and/or S waves through the crust are varied. This would imply that fine crustal structure derived from a matching of peak positions of observed spectral ratios with theoretical transfer function ratios, as is commonly practiced, is not very meaningful. This limitation in the application of the spectral ratio method for detailed crustal structure is demonstrated using two recent applications of this technique.     

Ground tilt variations in the Klyuchevskoi Volcano Area, Kamchatka

We consider the results of ground tilt observations in the area of Klyuchevskoi Volcano, Kamchatka at the Klyuchi and Apakhonchich stations using photoelectric tiltmeters. An anomalous tilt was recorded during a period of increased activity in the summit crater of Klyuchevskoi Volcano in November 1979. In January and February 1980 three more cases of anomalous tilting before the volcano’s active periods were observed. The tilts exhibit some common kinematic features that are quite consistent with the activity periods. Various disturbing influences were estimated as affecting the observations of tilts related to seismic and volcanic events. For the first time in Kamchatka, the parameters of the five principal elastic-tide waves have been determined. Sea tides exerted an indirect effect on the amplitude factors γ(M2) on the E-W component at both sites to decrease them relative to the global value, γ(M2) = 0.7. We investigated the influence of sea tides on the elastic solid earth tide along the Trans-Kamchatka and Kola traverses. The observed and theoretical γ(M2) factors at both traverses situated in different geodynamic areas are in approximate agreement.     

The 2010 Chilean Tsunami Off the West Coast of Canada and the Northwest Coast of the United States

The major (M _w = 8.8) Chilean earthquake of 27 February 2010 generated a trans-oceanic tsunami that was observed throughout the Pacific Ocean. Waves associated with this event had features similar to those of the 1960 tsunami generated in the same region by the Great (M _w = 9.5) 1960 Chilean Earthquake. Both tsunamis were clearly observed on the coast of British Columbia. The 1960 tsunami was measured by 17 analog pen-and-paper tide gauges, while the 2010 tsunami was measured by 11 modern digital coastal tide gauges, four NEPTUNE-Canada bottom pressure recorders located offshore from southern Vancouver Island, and two nearby open-ocean DART stations. The 2010 records were augmented by data from seven NOAA tide gauges on the coast of Washington State. This study examines the principal characteristics of the waves from the 2010 event (height, period, duration, and arrival and travel times) and compares these properties for the west coast of Canada with corresponding properties of the 1960 tsunami. Results show that the 2010 waves were approximately 3.5 times smaller than the 1960 waves and reached the British Columbia coast 1 h earlier. The maximum 2010 wave heights were observed at Port Alberni (98.4 cm) and Winter Harbour (68.3 cm); the observed periods ranged from 12 min at Port Hardy to 110–120 min at Prince Rupert and Port Alberni and 150 min at Bamfield. The open-ocean records had maximum wave heights of 6–11 cm and typical periods of 7 and 15 min. Coastal and open-ocean tsunami records revealed persistent oscillations that “rang” for 3–4 days. Tsunami energy occupied a broad band of periods from 3 to 300 min. Estimation of the inverse celerity vectors from cross-correlation analysis of the deep-sea tsunami records shows that the tsunami waves underwent refraction as they approached the coast of Vancouver Island with the direction of the incoming waves changing from an initial direction of 340° True to a direction of 15° True for the second train of waves that arrived 7 h later after possible reflection from the Marquesas and Hawaiian islands.     

In situ Measurements of Tide Gauge Response and Corrections of Tsunami Waveforms from the Niigataken Chuetsu-oki Earthquake in 2007

Linear and nonlinear responses of ten well-type tide gauge stations on the Japan Sea coast of central Japan were estimated by in situ measurements. We poured water into the well or drained water from the well by using a pump to make an artificial water level difference between the outer sea and the well, then measured the recovery of water level in the well. At three tide gauge stations, Awashima, Iwafune, and Himekawa, the sea-level change of the outer sea is transmitted to the tide well instantaneously. However, at seven tide gauge stations, Nezugaseki, Ryotsu, Ogi, Teradomari, Banjin, Kujiranami, and Naoetsu, the sea-level change of the outer sea is not always transmitted to the tide well instantaneously. At these stations, the recorded tsunami waveforms are not assured to follow the actual tsunami waveforms. Tsunami waveforms from the Niigataken Chuetsu-oki Earthquake in 2007 recorded at these stations were corrected by using the measured tide gauge responses. The corrected amplitudes of the first and second waves were larger than the uncorrected ones, and the corrected peaks are a few minutes earlier than the uncorrected ones at Banjin, Kujiranami, and Ogi. At Banjin, the correction was significant; the corrected amplitudes of the first and second upward motion are +103 cm and +114 cm, respectively, while the uncorrected amplitudes were +96 cm and +88 cm. At other tide gauge stations, the differences between the uncorrected and corrected tsunami waveforms were insignificant.     

Observations of semidiurnal internal tidal currents off central Chile (36.6°S)

Observations of semidiurnal internal tidal currents from three moorings deployed on the continental shelf off central Chile during summer and winter of 2005 are reported. The spectra of the baroclinic currents showed large peaks at the semidiurnal band with a dominant counterclockwise rotation, which was consistent with internal wave activity. The amplitude of the barotropic tidal currents varied according to the spring–neap cycle following the sea level fluctuations. In contrast, the amplitudes of the internal tide showed high spatial-temporal variability not directly related to the spring–neap modulation. Near the middle of the continental shelf and near the coast (San Vicente Bay) the variance of the semidiurnal baroclinic current is larger than the variance of its barotropic counterpart. The vertical structure of the baroclinic tidal current fluctuations was similar to the structure of the first baroclinic internal wave mode. In general, in the three study sites the variance of the baroclinic current was larger near the surface and bottom and tended to show a minimum value at mid depths. Kinetic energy related to semidiurnal internal waves was larger in winter when stratification of the water column was stronger. During summer, upwelling and the decrease of freshwater input from nearby rivers reduced the vertical density stratification. The amplitude of the semidiurnal internal tide showed a tendency to be enhanced with increasing stratification as observed in other upwelling areas. The continental shelf break and submarine canyons, which limit the continental shelf in the alongshore direction, represent near-critical slopes for the semidiurnal period and are suggested to be the main internal tide generation sites in the study region.     

A possible cause for the generation of unusually strong 20- and 30-hour oscillations in the neutral wind of the lower thermosphere

The harmonic relationship between the diurnal and semidiurnal tides gives rise to an elementary mathematical relationship that has intriguing consequences for secondary waves produced by non-linear interactions between the diurnal tide and planetary waves. A speculative theory is developed which predicts that, under certain conditions, these secondary waves can be amplified by non-linear interaction with the semidiurnal tide. A peculiar feature of dynamics in the MLT region above Bulgaria is the presence of strong oscillations with periods near 20 and 30 h, especially in the zonal wind component. Observational evidence from a meteor radar at Yambol, Bulgaria suggests that the 20- and 30-h signals are produced as the result of non-linear interactions of the type proposed by the novel theory.