Lunar perturbations in geomagnetic field and in the characteristics ofF-region over huancayo

Summary The lunar daily (L) and lunar monthly (M) variations in horizontal magnetic field (H), maximum electron density (N _max ), height of peak ionisation (h _max ), semi-thickness (y _m ) of theF ₂ layer and total electron content (N _t ) at Huancayo for the period January 1960 to December 1961 are described. The lunar tidal variations inh _max follow sympathetically the variations inH such that an increase of magnetic field causes the raising of height of peak ionisation. Lunar tides inN _max are opposite in phase to that ofh _max with a delay of about 1–2 hours, suggesting that an increase of height causes a decrease in maximum electron density. The lunar tides in semi-thickness are very similar in phase to that inh _max . The lunar tidal effects in any of the parameters are largest inD-months and least inJ-months. The amplitude of lunar tides in maximum electron density seems to increase with increasing height whereas the phase seems to be constant with height. It is concluded that lunar tides in the ionospheric parameters at magnetic equator are greatly controlled by the corresponding geomagnetic variations.Presented at the Third International Symposium on Equatorial Aeronomy, Ahmedabad, 3–10 February 1969.     

Lunar tidal componentsN 1 andO 2 in the atmospheric pressure

Summary The lunar tidal componentsO ₁(p) andN ₂(p) in the barometric pressure are determined for several observatories for which long series of data are available in machine readable form. AlsoN ₂(p) results are derived from some earlier analyses. The results are compared with those predicted by equilibrium tidal theory.This paper was presented at the General Scientific Assembly of I.A.G.A., held in Madrid in September 1969.     

Tidal currents in the central Great Barrier Reef

Observations at 8 sites in the outer central Great Barrier Reef show M₂, S₂, K₁, and O₁ tidal currents flow directly off-shelf (northeast), when the corresponding tide at Townsville is at zero height and falling, with typical amplitudes of 12, 6, 3, and 2 cm s^?1. On the slope (at 300 m depth), the vertically averaged long-shelf component was small. On the shelf, the eccentricity of the tidal ellipses decreases shoreward and the tidal ellipses rotate anticlockwise. The major axes of the tidal ellipses tilt left of cross-shelf, especially for the diurnal constituents. There is satisfactory agreement between the observed and modelled cross-shelf currents. The long-shelf velocity is sensitive to the long-shelf changes in amplitude and phase of the tide heights and high quality tidal data for open boundary conditions will be required if numerical models are to model these currents satisfactorily.     

Local contributions to the M2 lunar geomagnetic variations in the South West of England

By comparing the M₂ lunar geomagnetic variations of 12.42 h period at Sidmouth and Exeter, it is shown that local concentrations of the electric currents, induced by sea tides in the seas and oceans around the U.K., can give a significant contribution to the M₂ variations at the two observatories.     

Seasonal variation of the <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript> tide

The seasonal cycle of the main lunar tidal constituent M ₂ is studied globally by an analysis of a high-resolution ocean circulation and tide model (STORMTIDE) simulation, of 19 years of satellite altimeter data, and of multiyear tide-gauge records. The barotropic seasonal tidal variability is dominant in coastal and polar regions with relative changes of the tidal amplitude of 5–10 %. A comparison with the observations shows that the ocean circulation and tide model captures the seasonal pattern of the M ₂ tide reasonably well. There are two main processes leading to the seasonal variability in the barotropic tide: First, seasonal changes in stratification on the continental shelf affect the vertical profile of eddy viscosity and, in turn, the vertical current profile. Second, the frictional effect between sea-ice and the surface ocean layer leads to seasonally varying tidal transport. We estimate from the model simulation that the M ₂ tidal energy dissipation at the sea surface varies seasonally in the Arctic (ocean regions north of 60°N) between 2 and 34 GW, whereas in the Southern Ocean, it varies between 0.5 and 2 GW. The M ₂ internal tide is mainly affected by stratification, and the induced modified phase speed of the internal waves leads to amplitude differences in the surface tide signal of 0.005–0.0150 m. The seasonal signals of the M ₂ surface tide are large compared to the accuracy demands of satellite altimetry and gravity observations and emphasize the importance to consider seasonal tidal variability in the correction processes of satellite data.     

Effect of stratification on tidal circulation over the Scotian Shelf and Gulf of St. Lawrence: a numerical study using a three-dimensional shelf circulation model

A three-dimensional shelf circulation model is used to examine the effect of seasonal changes in water-column stratification on the tidal circulation over the Scotian Shelf and Gulf of St. Lawrence. The model is driven by tidal forcing specified at the model’s lateral open boundaries in terms of tidal sea surface elevations and depth-averaged currents for five major tidal constituents (M₂, N₂, S₂, K₁, and O₁). Three numerical experiments are conducted to determine the influence of baroclinic pressure gradients and changes in vertical mixing, both associated with stratification, on the seasonal variation of tidal circulation over the study region. The model is initialized with climatological hydrographic fields and integrated for 16 months in each experiment. Model results from the last 12 months are analyzed to determine the dominant semidiurnal and diurnal tidal components, M₂ and K₁. Model results suggest that the seasonal variation in the water-column stratification affects the M₂ tidal circulation most strongly over the shelf break and over the deep waters off the Scotian Shelf (through the development of baroclinic pressure gradients) and along Northumberland Strait in the Gulf of St. Lawrence (through changes in vertical mixing and bottom stress). For the K₁ constituent, the baroclinic pressure gradient and vertical mixing have opposing effects on the tidal circulation over several areas of the study region, while near the bottom, vertical mixing appears to play only a small role in the tidal circulation.     

Modelling tidally induced sediment-transport paths over the northwest European shelf: the influence of sea-level reduction

A three-dimensional model covering the northwest European Shelf and part of the adjacent Atlantic Ocean is used to examine the influence of water depth change upon the distribution of maximum tidal bed stress. The direction of bed stress is an indicator of sediment movement as bed load and various regions of convergence and divergence in good agreement with observations are identified. Calculations are performed with water depths reduced by 35 m, corresponding to 10 000 years before present (B.P.). Initially, the model is forced by only the M₂ tide, although subsequently five constituents, namely M₂, S₂, N₂, K₁ and O_1, are used for tidal forcing. Although the distribution of extreme bed stresses computed with only M₂ tidal forcing is comparable to that computed with five tides, the additional tidal constituents modify the magnitude of the bed stress. In particular the diurnal tides show regions of local enhanced current amplitude in the shelf-edge region with corresponding changes in bed stress. When water depths are reduced such that the North Sea and English Channel are separated, then there is a significant change in the tidal distribution in the shallow Southern Bight which influences bed-stress distributions and hence bed-load sediment transport in the area. Besides changes in shallow regions, the distribution of tides at the shelf edge is affected. A discussion of the limitations of the present coarse-grid model in shelf-edge regions and how it can be used to provide boundary conditions for limited-area three-dimensional models that can include stratification is presented. Also the importance of stratification for sediment movement at the shelf edge is briefly discussed.Responsible Editor: Phil Dyke     

A model for tides and currents in the English Channel and southern North Sea

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O₁, K₁, M₂, S₂, N₂, K₂, M₄, MS₄, MN₄, M₆, and 2MS₆.     

Is the abnormal response of the tide at the frequency of S2 really due to radiational effects?

The equilibrium ratios of the major solar component of the tide S₂ and of the component K₂, which have very close frequencies, seldom follow a linear trend when one extrapolates from that of the lunar component M₂. This is due to the different damping of the resultant of S₂ and K₂ during their six-month interference cycle, compared to that of the other components: it gives to K₂ a value larger than expected, while the reverse hold for S₂. It is unlikely that radiational effects are the cause of such behaviour as is currently believed.     

M<Subscript>2</Subscript> tidal dynamics in Bohai and Yellow Seas: a hybrid data assimilative modeling study

A high-resolution hybrid data assimilative (DA) modeling system is adapted to study the M₂ barotropic tidal characteristics and dynamics in the Bohai and Yellow Seas. In situ data include tidal harmonics extracted from both coastal sea level and bottom pressure observations. The hybrid DA system consists of both forward and inverse models. The former is three-dimensional, finite-difference, nonlinear Regional Ocean Modeling System (ROMS). The latter is a three-dimensional, linearized, frequency-domain, finite-element model TRUXTON. The DA system assimilates in situ observations via the inversion of the barotropic tidal open boundary conditions (OBCs). Model skill is evaluated by comparing misfits between the observed and modeled tidal harmonics. The assimilation scheme is found effective and efficient in correcting the tidal OBCs, which in turn improves ROMS tidal solutions. Up to 50% reduction of model/data misfits is achieved after data assimilation. M₂ co-tidal maps constructed from the posterior (data assimilative) ROMS solutions agree well with observational analysis of (Fang et al. 2004). Detailed analyses on tidal mixing, residual current, energy flux, dissipation, and momentum term balance dynamics are performed for M₂ constituent, revealing complex M₂ tidal characteristics in the study region and the important role of coastal geometry and topography in affecting regional tidal dynamics.     

Evidence for tidal triggering on the earthquakes of the Hellenic Arc,Greece

In this paper we investigate the tidal triggering evidence on the earthquakes of the seismic area of the Hellenic Arc using the Hist(ogram)Cum(mulation) method. We analyze the series of the earthquakes occurred in the area which is confined by the longitudes 22° and 28°E and latitudes 34° and 36°N in the time period from 1964 to 2012. In this time period 16,137 shallow and of intermediate depth earthquakes with M_L up to 6.0 and 1,482 deep earthquakes with M_L up to 6.2 occurred. The result of the this analysis indicate that the monthly variation of the frequencies of earthquake occurrence is in accordance with the period of the tidal lunar monthly variations, and the same happens with the corresponding daily variations of the frequencies of earthquake occurrence with the diurnal luni-solar (K1) and semidiurnal solar (S2) tidal variations. These results are in favor of a tidal triggering process on earthquakes when the stress in the focal area is near the critical level.     

Generation of overtides and compound tides in Amazon estuary

Tidal propagation in estuaries is affected by friction and fresh water discharge, besides changes in the depth and morphology of the channel. Main distortions imply variations in the mean water level and asymmetry. Tidal asymmetry can be important as a mechanism for sediment accumulation and turbidity maximum formation in estuaries, while mean water level changes can affect navigation depths. Data from several gauges stations from the Amazon estuary and the adjacent coast were analyzed and a 2DH hydrodynamic model was configured in a domain covering the continental shelf up to the last section of the river where the tidal signature is observed. Based on data, theoretical and numerical results, the various influences in the generation of estuarine harmonics are presented, including that of fresh water discharge. It is shown that the main overtide, M₄, derived from the most important astronomic component in the Amazon estuary, M₂, is responsible for the tidal wave asymmetry. This harmonic has its maximum amplitude at the mouth, where minimum depths are found, and then decreases while tide propagates inside the estuary. Also, the numerical results show that the discharge does not affect water level asymmetry; however, the Amazon river discharge plays an important role in the behavior of the horizontal tide. The main compound tide in Amazon estuary, Msf, generated from the combination of the M₂ and S₂, can be strong enough to provoke neap low waters lower than spring ones. The results show this component increasing while going upstream in the estuary, reaching a maximum and then slightly decaying.     

Tidal friction for semidiurnal tides

The quadratic law of bottom friction demands an increased frictional coefficient for the S₂ and N₂ tides with respect to a dominant M₂ tidal signal. A numerical model of the semidiurnal tides in the northeast Atlantic gives an increase in friction of ∼35% for the N₂, S₂ and K₂ tides with respect to the M₂ tide and this value is close to a theoretically derived estimate for the region, providing confirmation of the general widescale applicability of the quadratic friction law. Small differences in friction also occur for the N₂, S₂ and K₂ tides and this is attributed to the interaction of the L₂ and μ₂ tides with the M₂ tide in the presence of quadratic friction. Energy dissipation relationships, anomalous K₂/S₂ amplitude ratios and the role of quadratic friction on 18.6 year variations of semidiurnal forcing are examined.     

Fine grid tidal modeling of the Yellow and East China Seas

A fine grid tidal modeling experiment is carried out in order to investigate the tidal regimes for major five tidal constituents, the nonlinear tidal phenomena in terms of M₄ and MS₄ generation, and the independent tide by the tide generating force in the Yellow and East China Seas (YECS). In this study a two-dimensional numerical model based upon a subgrid-scale (SGS) stress modeling technique is used with the tide generating force included. The model was validated with recently observed tide and current data. The calculated tidal charts for tidal elevation show a generally good agreement with existing ones, with more accurate feature of the M₂ cotidal chart in comparison with both the observed data and the existing tidal charts. A careful comparison of the computed diurnal amplitude with observations suggests that the diurnal constituents seem to be overdamped especially in the Kyunggi Bay region, for the case when quadratic bottom friction law is used.Propagation features of the M₄(MS₄) tides are discussed in the YECS, based upon the analyses of the observed and calculated results. The amphidromic system of the M₄ is quite complicated and one noticeable characteristic is that the propagation direction of the M₄ tidal wave along the west coast of Korean peninsula is opposite to that of the M₂ tidal wave. This result coincides with observations. The propagation feature of the MS₄ is almost similar to that of the M₄, but with lesser amplitude. The responses of the M₄ tidal features to momentum diffusion term and depth-dependent form of the friction coefficient are also discussed.It is also shown that when the independent tide (Defant, 1960) arising from tide generating force (TGF) coexists with tidal waves (co-oscillating tide) arising from external boundary forcing, the TGF tidal waves are dissipated and their amphidromes tend to move westward. This may be interpreted as a process whereby the incident and reflected TGF tidal waves are damped by co-oscillating tide arising from external force at open boundaries. The TGF amplitude is found to be up to 10 cm and 4 cm in the Kyunggi Bay for the M₂ and S₂ constituents while those for all diurnal constituents are less than 1 cm over the entire model domain.     

Assimilation of altimetry data for nonlinear shallow-water tides: Quarter-diurnal tides of the Northwest European Shelf

Non-linear tidal constituents, such as the overtide M₄ or the compound tide MS₄, are generated by interaction in shallow seas of the much larger astronomically forced “primary” tidal constituents (e.g., M₂, S₂). As such, errors in modeling these “secondary” shallow-water tides might be expected to be caused first of all by errors in modeling the primary constituents. Thus, in the context of data assimilation, observations of primary-constituent harmonic constants can indirectly constrain shallow-water constituents. Here we consider variational data assimilation for primary and secondary tidal constituents as a coupled problem, using a simple linearized perturbation theory for weak interactions of the dominant primary constituents. Variation of the resulting penalty functional leads to weakly non-linear Euler–Lagrange equations, which we show can be solved approximately with a simple two-stage scheme. In the first stage, data for the primary constituents are assimilated into the linear shallow water equations (SWE), and the resulting inverse solutions are used to compute the quadratic interactions in the non-linear SWE that constitute the forcing for the secondary constituents. In the second stage, data for the compound or overtide constituent are assimilated into the linear SWE, using a prior forced by the results of the first stage. We apply this scheme to assimilation of TOPEX/Poseidon and Jason altimetry data on the Northwest European Shelf, comparing results to a large set of shelf and coastal tide gauges. Prior solutions for M₄, MS₄ and MN₄ computed using inverse solutions for M₂, S₂, and N₂ dramatically improve fits to validation tide gauges relative to unconstrained forward solutions. Further assimilation of along-track harmonic constants for these shallow-water constituents reduces RMS differences to below 1 cm on the shelf, approaching the accuracy of the validation tide gauge harmonic constants.     

Sea level fluctuations on the east coast of Taiwan that overlie continental shelf break

Captured CO₂ could be deliberately injected into the ocean at great depth, where most of it would remain isolated from the atmosphere for centuries. CO₂ can be transported via pipeline or ship for release in the ocean or on the sea floor. No matter what for medium depth or deep sea, it appears that a potential area exists between 122–122.5°E and 21.8–22.3°N for CO₂ sequestration. The east coast of Taiwan can be a candidate for CO₂ temporary storage or transmitted plant. To have whole picture of assessment of sea level fluctuation, a completed statistical summary of seasonal sea level at six tidal gauge stations along the east coast of Taiwan is provided herein. Seasonal sea level time series is analyzed using spectral analysis in frequency domain to identify periodic component and phase propagation, especially for the astronomical-driven tidal effects. It identifies that the semi-diurnal and diurnal components in the resultant time series are related to astronomical tides M₂, and K₁ and O₁, respectively. It demonstrates a full analysis of sea level variations, and results can be useful when construction of testing or operating facilities on sea surface becomes desirable in the future.     

Determination of the long period tidal waves in the GGP superconducting gravity data

Several results about the long period (LP) tidal waves are obtained by the analysis of series of superconducting gravity data, provided by the Global Geodynamics Project (GGP). The most important result is the determination of a single group called LPMF, composed by all LP tides but representing accurately the parameters of the M_f wave. As the LP tidal generating potential is vanishing at latitudes ±35°15′52″ we cannot determine accurate tidal amplitude factors for the stations located between ±40° and ±30°. However, it is still possible to obtain tidal residual vectors and compare them with oceanic tidal loading computations. For 15 stations the NAO99 oceanic model is giving a coherent picture. For nine stations with M_f amplitude larger than 3 μgal (1 μgal = 10 nm s⁻²) a global analysis is obtained by introducing the loading effect of the ocean directly in the observation equations. The mean amplitude factor obtained for LPMF is larger than expected from the models and there is a significant phase lag, showing the imperfection of the tidal oceanic models for M_f. Other new result is the first separate estimation of the parameters of the LP tides, generated by the tidal potential of third degree, dominated by a Lunar declinational monthly wave, called here 3M_md. Due to their small amplitudes (under 1 μgal) these waves are practically hidden by the noise. Nevertheless, the quality of the data and the flexibility of the VAV analysis method [Venedikov, A.P., Arnoso, J., Vieira, R., 2001. Program VAV/2000 for tidal analysis of unequally spaced data with irregular drift and colored noise. J. Geodetic Soc. Jpn. 47 (1), 281–286; Venedikov, A.P., Arnoso, J., Vieira, R., 2003. VAV: a program for tidal data processing. Comput. Geosci. 29, 487–502.] allow getting significant results, in agreement with the theory of the Earth deformation by the tidal potential of third degree.     

Tidal and secular tilt from an earthquake zone: thresholds for detection of regional anomalies

Tiltmeter data from an array of three boreholes at the Charlevoix observatory in the Charlevoix seismic region of Que´bec have been analysed for evidence of tectonically related signals. The secular tilt is dominated by water table induced effects which can be substantially removed by linear regression of the water level on the tilt. Short-term (days to months) anomalies are shown to be detectable at the 0.3 μrad to 1 μrad level depending on the depth of the measurement. Long-term changes in the linear drift as small as 0.1 μrad/yr would be detectable in all of the boreholes.Large spatial anomalies in the mean tidal admittance among boreholes preclude its use in refining either models of the regional crustal structure or the adjacent marine tide distribution. Strongly coherent time variations in the tidal admittance among the observations of all the major tidal constituents are shown to be generated by corresponding variations in marine tidal loading in the St. Lawrence estuary. Diurnal band variations are closely correlated with the tide gauge data. The semi-diurnal constituents show a weaker correlation because of the complex spatial pattern within the estuary of time variations in this band. Inspection of the residual admittance variations for the M₂ and O₁ constituents demonstrates that the thresholds for detecting tectonic tidal tilt anomalies are ±2% and ±5–8%, respectively.The level of earthquake activity in the Charlevoix seismic zone throughout the period of the borehole tiltmeter experiment was sufficiently low that no significant tilt anomalies were expected or were undeniably detected.     

The oceanic tides in the South Atlantic Ocean

The finite element ocean tide model of Le Provost and Vincent (1986) has been applied to the simulation of the M₂ and K₁ components over the South Atlantic Ocean. The discretisation of the domain, of the order of 200 km over the deep ocean, is refined down to 15 km along the coasts, such refinement enables wave propagation and damping over the continental shelves to be correctly solved. The marine boundary conditions, from Dakar to Natal, through the Drake passage and from South Africa to Antarctica, are deduced from in situ data and from Schwiderski’s solution and then optimised following a procedure previously developed by the authors. The solutions presented are in very good agreement with in situ data: the root mean square deviations from a standard subset of 13 pelagic stations are 1.4 cm for M₂ and 0.45 cm for K₁, which is significantly better overall than solutions published to date in the literature. Zooms of the M₂ solution are presented for the Falkland Archipelago, the Weddell Sea and the Patagonian Shelf. The first zoom allows detailing of the tidal structure around the Falklands and its interpretation in terms of a stationary trapped Kelvin wave system. The second zoom, over the Weddell Sea, reveals for the first time what must be the tidal signal under the permanent ice shelf and gives a solution over that sea which is generally in agreement with observations. The third zoom is over the complex Patagonian Shelf. This zoom illustrates the ability of the model to simulate the tides, even over this area, with a surprising level of realism, following purely hydrodynamic modelling procedures, within a global ocean tide model. Maps of maximum associated tidal currents are also given, as a first illustration of a by-product of these simulations.     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.