Tidal Phase Lag Research Articles

The sensitivity of tidal asymmetry descriptors in the Ems estuary

Tidal asymmetry in estuaries and other tidally dominated coastal systems is commonly evaluated to assess system states or their development. Based on different methods, local states are classified as either flood or ebb dominant. An increasing number of descriptors for deriving tidal asymmetry in recent years calls for a comparison and discussion of their sensitivity on input data and its quality. We compared tidal asymmetry from water level and current velocity using various descriptors that deduce from harmonic, ratio, and skewness methods. Computed from one-year measurements at different stations along the Ems estuary, their comparability was enabled by a new approach of scaling. Our results on the variation of sampling intervals demonstrated a highly site-specific sensitivity of the descriptors that led up to changes in the asymmetry direction in tidal duration asymmetry and phase lag. The slack water asymmetry appeared most sensitive to the studied parameter settings. As expected, variability of tidal asymmetry reduced with an increasing number of analyzed tides. At the same time, uncertainty from the asymmetry during spring or neap phases compared to spring-neap periods remained in all analyzed descriptors. Hence, the characterization of the estuary in terms of flood- or ebb-dominance depends critically on the quality and extent of the input data. For all parameter settings, the impact of river discharge on tidal asymmetry was pronounced but varied depending on the location in the estuary. The actual characterization of the effect of asymmetry, e.g., on sediment transport, is not conducted in this study. We propose that this requires a more comprehensive dataset, such as depth and cross-sectional variability of currents and sediment concentrations.

Hydraulic head fluctuations in an intermediate depth coastal surface aquifer

Tides and storm surges are important drivers of groundwater circulation and fluxes in coastal aquifers. However, few field studies have characterized the response of the coastal aquifer to both forcings. Here, three years of hydraulic head observations in a roughly 20-m deep barrier island surface aquifer are used to investigate the inland propagation of fluctuations driven by ocean water-level changes owing to diurnal and semi-diurnal tides and storm-induced surge and wave-driven setup. Similar to prior observations, the observed rate of amplitude attenuation of the hydraulic head fluctuations is higher than the inland increase in phase lag for the tidally-driven head fluctuations. Additionally, tidal hydraulic head fluctuations deeper in the aquifer lead those nearer the surface of the aquifer. In contrast, storm surges with periods of several days have similar rates of amplitude attenuation and inland increase in phase lags, and hydraulic head fluctuations are roughly depth uniform. A nonlinear, intermediate aquifer-depth theory (not previously compared with field observations) describes the inland and vertical changes of tidal amplitudes and phase lags, and collapses to the linear solution for long period fluctuations, consistent with the storm surge observations. The diffusivity estimated by fitting intermediate depth solutions to the observed tidal amplitude attenuation and rate of inland phase lag is consistent with the aquifer properties, providing a method to characterize aquifers using coastal head observations. Numerical model simulations neglecting capillary effects, hysteresis, and vertical layering (which can cause discrepancies between amplitude attenuation and phase lag evolution) are similar to the observations and support the importance of the depth of the aquifer relative to the wavelength of the hydraulic head fluctuations.

Sensitivity analysis of polar orbiter motion to lunar viscoelastic tidal deformation

We investigate the impact of viscoelastic tidal deformation of the Moon on the motion of a polar orbiter. The dissipative effects in the Moon’s interior, i.e., tidal phase lags, are modeled as Fourier series sampled at given frequencies associated with linear combinations of Delaunay arguments, the fundamental parameters describing the lunar motion around the Earth and the Sun. We implement the tidal model to evaluate the temporal lunar gravity field and the induced perturbation on the orbiter. We validate the numerical scheme via a frequency analysis of the perturbed orbital motion. We show that, in the case of the Lunar Reconnaissance Orbiter at a low altitude of less than 200 km, the main lunar tides and hence the potential Love numbers around the monthly and some multiple frequencies are dynamically separable. The omission of those effects in practice introduces a position error at the level of a few decimeters within 10 days.

Probing the Icy Shell Structure of Ocean Worlds with Gravity–Topography Admittance

Abstract The structure of the icy shells of ocean worlds is important for understanding the stability of their underlying oceans as it controls the rate at which heat can be transported outward and radiated to space. Future spacecraft exploration of the ocean worlds (e.g., by NASA’s Europa Clipper mission) will allow for higher-resolution measurements of gravity and shape than currently available. In this paper, we study the sensitivity of gravity–topography admittance to the structure of icy shells in preparation for future data analysis. An analytical viscous relaxation model is used to predict admittance spectra given different shell structures determined by the temperature-dependent viscosity of a tidally heated, conductive shell. We apply these methods to the ocean worlds of Europa and Enceladus. We find that admittance is sensitive to the mechanisms of topography support at different wavelengths and estimate the required gravity performance to resolve transitions between these mechanisms. We find that measuring admittance would be complementary to ice-penetrating radar in constraining shell thickness as it would cover the cases for which a direct ice–ocean interface detection is less favorable with radar, i.e., for warmer and thicker shells. Finally, we find that admittance may be used to constrain the tidal dissipation within the icy shell, which would be complementary to a more demanding measurement of the tidal phase lag.

Drivers of cross-shore chenier dynamics off a drowning coastal plain

A chenier is a beach ridge, consisting of sand and/or shells, overlying a muddy substrate. In this paper, we explore the cross-shore dynamics of cheniers in their ‘active’ phase, i.e. the phase between their formation and their landing on the shore and can no longer be reached by daily wave and tidal influences. While cheniers described in literature are known to only migrate onshore until they reach a stable position with their crest level above tidal influences, observations in Demak suggest the existence of an alternative stable state, highly dynamic on the short term, but stable on the longer term. To explore this alternative stable state, we developed an idealised chenier model to investigate cross-shore chenier dynamics under daily wave and tidal influences. The model is able to predict both onshore and offshore migration; onshore migration is mainly driven by wave action, while offshore migration is induced by a tidal phase lag, or the effect of the storm season. For certain combinations of waves, tide (incl. phase lag) and a storm season effect, the model predicts a dynamically stable chenier. In absence of a phase lag and storm season effect, the model yields a ‘classic’ stable chenier that welds onto the shoreline by onshore migration.

The Determination of the Rotational State and Interior Structure of Venus with VERITAS

Abstract Understanding the processes that led Venus to its current state and will drive its future evolution is a major objective of the next generation of orbiters. In this work we analyze the retrieval of the spin vector, the tidal response, and the moment of inertia of Venus with VERITAS, a NASA Discovery-class mission. By simulating a systematic joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar, we show that VERITAS will provide accuracies (3σ) in the estimates of the tidal Love number k 2 to 4.6 × 10−4, its tidal phase lag to 0.°05, and the moment of inertia factor to 9.8 × 10−4 (0.3% of the expected value). Applying these results to recent models of the Venus interior, we show that VERITAS will provide much-improved constraints on the interior structure of the planet.

Ocean Tides near Hawaii from Satellite Altimeter Data. Part I

AbstractSufficient and accurate tide data are essential for analyzing physical processes in the ocean. A method is developed to spatially fit the tidal amplitude and phase lag data along satellite altimeter tracks near Hawaii and construct reliable cotidal charts by using the Chebyshev polynomials. The method is completely dependent on satellite altimeter data. By using the cross-validation method, the optimal orders of Chebyshev polynomials are determined and the polynomial coefficients are calculated by the least squares method. The tidal amplitudes and phase lags obtained by the method are compared with those from the Finite Element Solutions 2014 (FES2014), National Astronomical Observatory 99b (NAO.99b), and TPXO9 models. Results indicate that the method yields accurate results as its fitting results are consistent with the harmonic constants of the three models. The feasibility of this method is also validated by the harmonic constants from tidal gauges near Hawaii.

Determination of Venus’ Interior Structure with EnVision

The Venusian geological features are poorly gravity-resolved, and the state of the core is not well constrained, preventing an understanding of Venus’ cooling history. The EnVision candidate mission to the ESA’s Cosmic Vision Programme consists of a low-altitude orbiter to investigate geological and atmospheric processes. The gravity experiment aboard this mission aims to determine Venus’ geophysical parameters to fully characterize its internal structure. By analyzing the radio-tracking data that will be acquired through daily operations over six Venusian days (four Earth’s years), we will derive a highly accurate gravity field (spatial resolution better than ~170 km), allowing detection of lateral variations of the lithosphere and crust properties beneath most of the geological features. The expected 0.3% error on the Love number k2, 0.1° error on the tidal phase lag and 1.4% error on the moment of inertia are fundamental to constrain the core size and state as well as the mantle viscosity.

Tidal characteristics of South Africa

The tidal characteristics of South Africa are explored in the present study by means of a calibrated and validated regional numerical model. The coastal tidal characteristics and semi-diurnal resonance of the South African coastline have yet to be accurately quantified. Model development was conducted in the numerical code Delft 3D for a two year simulation period. A horizontal model resolution of 1/16th geographical degree was employed. The results were calibrated against long-term measured water levels provided by the South African Navy Hydrographic Office. Model validation was performed for each major constituent's amplitude and phase lag at nine coastal locations around the South African coastline. Regional, two-dimensional comparisons were also made between this study's model results and those of the data assimilative TPXO 8 African regional model. The tide was characterized in terms of constituent amplitude and phase lag, Form Factor and tidal ellipse eccentricity regional by means of map plots. The model was particularly sensitive to bathymetry-related friction and model resolution. Accurate model results were obtained, providing the first identification and quantification of the semi-diurnal coastal resonance around South Africa. The phase lag associated with the shallower shelf areas is also clearly observed with Form Factor calculations confirming the semi-diurnal dominance of the South African coastline. The intermediate and shallow water friction-induced phase lag of the mixed progressive and standing tidal wave is also mapped, together with the tidal current phase lags.

Tidal constraints on the interior of Venus

AbstractAs a prospective study for a future exploration of Venus, we compute the tidal response of Venus' interior assuming various mantle compositions and temperature profiles representative of different scenarios of Venus' formation and evolution. The mantle density and seismic velocities are modeled from thermodynamical equilibria of mantle minerals and used to predict the moment of inertia, Love numbers, and tide‐induced phase lag characterizing the signature of the internal structure in the gravity field. The viscoelasticity of the mantle is parameterized using an Andrade rheology. From the models considered here, the moment of inertia lies in the range of 0.327 to 0.342, corresponding to a core radius of 2900 to 3450 km. Viscoelasticity of the mantle strongly increases the potential Love number relative to previously published elastic models. Due to the anelasticity effects, we show that the possibility of a completely solid metal core inside Venus cannot be ruled out based on the available estimate of k2 from the Magellan mission (Konopliv and Yoder, 1996). A Love number k2 lower than 0.27 would indicate the presence of a fully solid iron core, while for larger values, solutions with an entirely or partially liquid core are possible. Precise determination of the Love numbers, k2 and h2, together with an estimate of the tidal phase lag, are required to determine the state and size of the core, as well as the composition and viscosity of the mantle.

A preliminary 1‐D model investigation of tidal variations of temperature and chlorinity at the Grotto mound, Endeavour Segment, Juan de Fuca Ridge

AbstractTidal oscillations of venting temperature and chlorinity have been observed in the long‐term time series data recorded by the Benthic and Resistivity Sensors (BARS) at the Grotto mound on the Juan de Fuca Ridge. In this study, we use a one‐dimensional two‐layer poroelastic model to conduct a preliminary investigation of three hypothetical scenarios in which seafloor tidal loading can modulate the venting temperature and chlorinity at Grotto through the mechanisms of subsurface tidal mixing and/or subsurface tidal pumping. For the first scenario, our results demonstrate that it is unlikely for subsurface tidal mixing to cause coupled tidal oscillations in venting temperature and chlorinity of the observed amplitudes. For the second scenario, the model results suggest that it is plausible that the tidal oscillations in venting temperature and chlorinity are decoupled with the former caused by subsurface tidal pumping and the latter caused by subsurface tidal mixing, although the mixing depth is not well constrained. For the third scenario, our results suggest that it is plausible for subsurface tidal pumping to cause coupled tidal oscillations in venting temperature and chlorinity. In this case, the observed tidal phase lag between venting temperature and chlorinity is close to the poroelastic model prediction if brine storage occurs throughout the upflow zone under the premise that layers 2A and 2B have similar crustal permeabilities. However, the predicted phase lag is poorly constrained if brine storage is limited to layer 2B as would be expected when its crustal permeability is much smaller than that of layer 2A.

Anelasticity across seismic to tidal timescales: a self-consistent approach

In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau et al. have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ∼20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q−1. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q−1 and its frequency dependence in studies that have treated Q−1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q−1) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau et al. into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.

Numerical study of sediment transport on a tidal flat with a patch of vegetation

To understand how vegetation canopies affect sediment transport on tidal flats, a numerical study of tidal flow and sediment transport on an idealized tidal flat with a patch of vegetation is conducted. The numerical model is firstly validated by laboratory measurements of flow and sediment deposition in a partially vegetated open channel. The idealized study shows that a finite patch of vegetation may produce circulation on the tidal flat with converging flow during flood and diverging flow during ebb. The vegetation patch can also generate a tidal phase lag between the vegetated and bare flats. Tidal currents in both zones are asymmetric, with stronger flood current in the vegetated zone and stronger ebb current on the bare flat. The duration of ebb is longer than that of flood. Computed sediment concentration on the bare flat is higher during ebb due to stronger ebb current and larger bottom shear stress. This is in contrast to the tidal flat without a vegetation canopy, where suspended sediment concentration is higher during flood. On the tidal flat without a vegetation canopy, landward net sediment transport occurs on the upper flat, while seaward net sediment transport occurs on the lower flat and subtidal region. On the partially vegetated tidal flat, however, net sediment transport on both the upper and lower flats are in seaward direction. It increases with increasing vegetation density. Alongshore net sediment flux converges inside the canopy and diverges on the bare flat. Sediment exchange rate between the vegetated and bare flats increases with decreasing vegetation density and sediment settling velocity.

HYDRODYNAMIC AND MORPHOLOGIC MODELING OF ALTERNATIVE DESIGN SCENARIOS FOR SHIPPAGAN GULLY, NEW BRUNSWICK CANADA

This paper describes a comprehensive study comprising field measurements and numerical modeling of hydrodynamic and sedimentary processes undertaken to help assess alternative engineering measures for promoting and maintaining a stable and safe navigation channel through a dynamic tidal inlet. Shippagan Gully is a dynamic tidal inlet located on the Gulf of St-Lawrence near Le Goulet, New Brunswick, Canada. The tidal lagoon transects the Acadian Peninsula, hence the flows through the inlet are controlled by the tidal phase lag between the two open boundaries. Due to the nature of this phase lag, the ebb flows through Shippagan Gully, which regularly exceed 2 m/s, are typically twice as strong as the flood flows. As a consequence of this imbalance, the hydrodynamic and sedimentary processes at the inlet, and the morphologic features produced by these processes, are strongly dominated by the ebb flows. Over the past decades, shipping activities through Shippagan Gully have been threatened due to sediment deposition along the east side of the inlet which has caused the channel to narrow and shift westward. The objective of the present study was to develop an improved numerical model of the hydrodynamic and sedimentary processes at Shippahan Gully, and then apply the model to assess different engineering interventions for stabilizing the inlet and improving navigation safety.

Analytical approach for predicting fresh water discharge in an estuary based on tidal water level observations

Abstract. As the tidal wave propagates into an estuary, the tidally averaged water level tends to rise in landward direction due to the density difference between saline and fresh water and the asymmetry of the friction. The effect of friction on the residual slope is even more remarkable when accounting for fresh water discharge. In this study, we investigate the influence of river discharge on tidal wave propagation in the Yangtze estuary with specific attention to residual water level slope. This is done by using a one-dimensional analytical model for tidal hydrodynamics accounting for the residual water level. We demonstrate the importance of the residual slope on tidal dynamics and use it to improve the prediction of the tidal propagation in estuaries (i.e. tidal damping, velocity amplitude, wave celerity and phase lag), especially when the influence of river discharge is significant. Finally, we develop a new inverse analytical approach for estimating fresh water discharge on the basis of tidal water level observations along the estuary, which can be used as a tool to obtain information on the river discharge that is otherwise difficult to measure in the tidal region.

Relationship between the Earth tidal factor and phase lag of groundwater levels in confined aquifers and the Wenchuan M s8.0 earthquake of 2008

This work focuses on variations of the Earth tidal factor and phase lag derived from groundwater observations before and after major earthquakes. It is based on an analysis of the data from four observational wells at boundaries between distinct active blocks of China mainland. These wells are also situated on several active fault zones and have exhibited considerable responses to the Wenchuan Ms8.0 earthquake of 2008 in China. We collected hourly records of water levels of these wells from 2007 to 2009 and processed these data for analysis. The tidal factors, phase lags, and phase-difference changes of tidal residuals of each well were calculated. We found that when the Wenchuan quake happened, the tidal factors of the 4 wells were changing rapidly, while their phase lags and phase differences of tidal residuals declined swiftly, which may reflect the stress and strain changes of the well-aquifer system during the seismic generation.

A methodology for the classification of estuary restoration areas: A management tool

Planning the recovery of estuarine areas represents a major challenge for environmental managers, who must find a balance between the desired environmental restoration, understood as the return to natural conditions, and the different socioeconomic uses currently borne by the estuaries. This work presents a methodology to optimize decision-making in accordance with the objectives which might arise in projects for the hydrodynamic restoration of estuaries. Socioeconomic issues are not considered in this study. The new approach is based on a classification of the zones to be restored according to characteristics representing their hydrodynamic performance and the possible morphodynamic effects of the restoration on the rest of the estuary. To achieve this, the four following parameters were chosen: (1) changes in tidal prism induced by restoration of that zone (ΔΩ), (2) the distance between the concession and the estuary inlet (L), (3) the tidal wave phase lag (φ) and (4) the flood potential of the restoration area (I). The classification combines self-organizing maps (SOM) and the K-means algorithm. The methodology was applied in a total of 139 areas (concessions) on ten estuaries along the entire coast of Cantabria (Northern Spain) where a Spanish Ministry of the Environment Recuperation Plan is under way. The results classify the 139 areas of restoration into five clusters. Empirical relationships were used to estimate the effects the restoration of each cluster may have on the estuary's various morphodynamic elements (cross-sectional area of the estuary mouth, area of tidal flats, volume of tidal channels and volume of the ebb tidal delta), giving managers an overall view of the potential effects of the restoration in each zone and providing a basis on which to plan these actions.

A solution for the correct interpolation of data across regions with abrupt changes in tidal phase-lag

This paper provides an explanation of an automated solution for correctly interpolating phase-lags across abrupt boundaries. Although an automated solution to this problem has existed for several years, this is not commonly known and so many researchers continue to perform corrections manually. Interpolation errors commonly occur when tidal propagation surfaces are generated for regimes with amphidromic points. General correction methods are manual, clunky and prone to operator error. The problem can be solved by applying a simple method to scalarize the phase-lag vectors pre-interpolation. This approach successfully and automatically generates correct tidal phase-lag interpolation values and may be applied to any surface mapping software used to interpolate phase-lags.

TIDAL DISSIPATION COMPARED TO SEISMIC DISSIPATION: IN SMALL BODIES, EARTHS, AND SUPER-EARTHS

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and self-gravitation of a body as a whole. For a qualitative estimate, we model the body with a homogeneous sphere and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and makes tidal damping less efficient in larger bodies. At high frequencies, competition between self-gravitation and rheology becomes more complex, though for sufficiently large superearths the same rule works: the larger the body, the weaker tidal damping in it. Being negligible for small terrestrial planets and moons, the difference between the seismic and tidal lagging (and likewise between the seismic and tidal damping) becomes very considerable for superearths. In those, it is much lower than what one might expect from using a seismic quality factor. The tidal damping rate deviates from the seismic damping rate especially in the zero-frequency limit, and this difference takes place for bodies of any size. So the equal in magnitude but opposite in sign tidal torques, exerted on one another by the primary and the secondary, go smoothly through zero as the secondary crosses the synchronous orbit. We describe the mantle rheology with the Andrade model, allowing it to lean towards the Maxwell model at the lowest frequencies. To implement this additional flexibility, we reformulate the Andrade model by endowing it with a free parameter which is the ratio of the anelastic timescale to the viscoelastic Maxwell time of the mantle. Some uncertainty in this parameter's frequency-dependence does not influence our principal conclusions.

조류 조화상수의 월변동성 완화 방법 고찰

This is a preliminary study of the feasibility of obtaining reliable tidal current harmonic constants, using one month of current observations, to verify the accuracy of a tidal model. An inference method is commonly used to separate out the tidal harmonic constituents when the available data spans less than a synodic period. In contrast to tidal constituents, studies of the separation of tidal-current harmonics are rare, basically due to a dearth of the long-term observation data needed for such experiments. We conducted concurrent and monthly harmonic analyses for tidal current velocities and heights, using 2 years (2006 and 2007) of current and sea-level records obtained from the Tidal Current Signal Station located in the narrow waterway in front of Incheon Lock, Korea. Firstly, the l-year harmonic analyses showed that, with the exception of M₂ and S₂ semidiurnal constituents, the major constituents were different for the tidal currents and heights. K₁, for instance, was found to be the 4th major tidal constituent but not an important tidal current constituent. Secondly, we examined monthly variation in the amplitudes and phase-lags of the S₂ and K₁ current-velocity and tide constituents over a 23-month period. The resultant patterns of variation in the amplitudes and phase-lags of the S₂ tidal currents and tides were similar, exhibiting a sine curve form with a 6-month period. Similarly, variation in the K₁ tidal constant and tidal current-velocity phase lags showed a sine curve pattern with a 6-month period. However, that of the K₁ tidal current-velocity amplitude showed a somewhat irregular sine curve pattern. Lastly, we investigated and tested the inference methods available for separating the K₂ and S₂ current-velocity constituents via monthly harmonic analysis. We compared the effects of reduction in monthly variability in tidal harmonic constants of the S₂ currentvelocity constituent using three different inference methods and that of Schureman (1976). Specifically, to separate out the two constituents (S₂ and K₂), we used three different inference parameter (i.e. amplitude ratio and phase-lag diggerence) values derived from the ₁-year harmonic analyses of current-velocities and tidal heights at (near) the short-term observation station and from tidal potential (TP), together with Schureman’s (1976) inference (SI). Results from these four different methods reveal that TP and SI are satisfactorily applicable where results of long-term harmonic analysis are not available. We also discussed how to further reduce the monthly variability in S₂ tidal current-velocity constants.