Non-tidal Signals Research Articles

Multiscale sea level variability on the western Bay of Bengal: A study using tide gauge and satellite observations

The study examines the tidal variability and intraseasonal oscillations (ISOs) of sea level using tide gauge observations collected during the year 2014 at four stations: Gardenreach, Paradeep, Kakinada, and Ennore along the western Bay of Bengal (BoB). In the first part, the tidal analysis of sea level data shows the dominance of M2 tides followed by S2, N2, K1, and O1 at all the stations. The tides are usually semidiurnal in nature over BoB, represented through the form factor, which is maximum over Ennore (0.21) and minimum over Gardenreach (0.10). The tidal amplitudes increase gradually northward along the western BoB due to interaction with the shallow continental shelf. The topography and coastal geometry also impact the shallow-water constituents (M4 and MS4) significantly at all the locations. Another noteworthy finding is the higher amplitude of M2 tide during the post-monsoon seasons because of the higher stratification of the water column. In the second part, the presence of different non-tidal signals from the residual sea level and altimetry gridded data are studied as well. The correlation coefficient between Sea Level Anomaly (SLA) data from altimetry and the Tide Gauge data are as high as 0.94, 0.91, and 0.90 at Paradeep, Kakinada and Ennore, respectively. The spectral analysis ensures the dominance of the signals with periodicity of 20–60 days in the BoB, which is probably caused due to the monsoon ISOs and Madden Julian Oscillations. The 10–20 days oscillations are also observed with significant amplitudes primarily at Gardenreach which attributes to the Quasi-Biweekly Oscillations. The signature of seasonally varying coastally trapped Kelvin Waves is also identified on the western BoB from both the satellite and Tide Gauge data. The strength of the intraseasonal variability significantly increases during negative Indian Ocean Dipole years with respect to the positive years. The study identified the usefulness of the sea level observation to monitor the multiscale variation within the tides to the interannual scales along the Indian coast.

Total water level prediction at continental scale: Coastal ocean

We demonstrate recent progress made in the simulation of total water level (TWL) at continental scale, using the coastal ocean of US East Coast/Gulf of Mexico coast as an example. A key difference between the continental-scale and small-scale modeling is that the former requires a more accurate vertical datum. Using a geoid-based datum (xGEOID20b), a satellite altimetry product, and a state-of-the-art 3D unstructured-grid model, we significantly improve the accuracy for TWL both near- and off-shore. The average root-mean-square error at all NOAA stations is 14 cm. The non-tidal signals are found to be sensitive to the representation of a large-scale current system near the boundary and extending the domain extent to accommodate this system improves these signals.

Gravity field recovery of inter-satellite links between Beidou navigation satellite system (BDS) and LEO based on geodesy and time reference in space (GETRIS)

The goal of this contribution is to construct the inter-satellite links (ISLs) between Global Navigation Satellite System (GNSS) and Low Earth Orbit (LEO) satellite to recover the Earth’s gravity field based on the concept of Geodesy and Time Reference in Space (GETRIS). Taking the constellation of the Beidou Navigation Satellite System (BDS) as an example, several types of high-low satellite-to-satellite tracking (H-L SST) modes combining BDS and GETRIS are used to research the tracking mode of high orbit satellites and the distribution of LEO satellite constellations to explore the optimal mode for gravity field recovery. The effects of multiple H-L SST modes on the accuracy of gravity field recovery are studied. In addition, the contribution of each error source is also analyzed. Finally, this study varies LEO satellite constellations to show reduced errors in the temporal gravity field solutions for the improved ISLs. The results showed that the Inclined GeoSynchronous Orbit (IGSO) satellite greatly improved the Geosynchronous orbit (GEO) satellite tracking LEO satellite mode in the high latitude regions. Compared with the Medium Earth Orbit (MEO) satellite tracking LEO satellite, the error of gravity field recovered by combining with GEO, IGSO and MEO can be reduced by 16 %. The largest error is the non-tidal signal, followed by the ocean tidal model difference, and the smallest is the instrument error. For a single LEO satellite, the combination model is more sensitive to the satellite orbital altitude, the cumulative error was decreased from 5.08 mm (550 km) to 0.33 mm (250 km). For LEO constellations, adding inclined orbit satellites can improve the accuracy of the solution to some extent. But the optimal solution can be obtained by the constellation composed of polar orbit satellites with different Right Ascension of Ascending Node (RAAN), the cumulative errors are 0.27 mm (two satellites), 0.19 mm (three satellites), and 0.19 mm (four satellites).

Sub-daily polar motion from GPS, GLONASS, and Galileo

We derive an empirical model of the sub-daily polar motion (PM) based on the multi-GNSS processing incorporating GPS, GLONASS, and Galileo observations. The sub-daily PM model is based on 3-year multi-GNSS solutions with a 2 h temporal resolution. Firstly, we discuss differences in sub-daily PM estimates delivered from individual GNSS constellations, including GPS, GLONASS, Galileo, and the combined multi-GNSS solutions. Secondly, we evaluate the consistency between the GNSS-based estimates of the sub-daily PM with three independent models, i.e., the model recommended in the International Earth Rotation and Reference Systems Service (IERS) 2010 Conventions, the Desai–Sibois model, and the Gipson model. The sub-daily PM estimates, which are derived from system-specific solutions, are inherently affected by artificial non-tidal signals. These signals arise mainly from the resonance between the Earth rotation period and the satellite revolution period. We found strong spurious signals in GLONASS-based and Galileo-based results with amplitudes up to 30 µas. The combined multi-GNSS solution delivers the best estimates and the best consistency of the sub-daily PM with external geophysical and empirical models. Moreover, the impact of the non-tidal spurious signals in the frequency domain diminishes in the multi-GNSS combination. After the recovery of the tidal coefficients for 38 tides, we infer better consistency of the GNSS-based empirical models with the new Desai–Sibois model than the model recommended in the IERS 2010 Conventions. The consistency with the Desai–Sibois model, in terms of the inter-quartile ranges of tidal amplitude differences, reaches the level of 1.6, 5.7, 6.3, 2.2 µas for the prograde diurnal tidal terms and 1.2/2.1, 2.3/6.0, 2.6/5.5, 2.1/5.1 µas for prograde/retrograde semi-diurnal tidal terms, for the combined multi-GNSS, GPS, GLONASS, and Galileo solutions, respectively.

The Effects of Non-TIDAL Components, Depth of Measurement and the Use of Peak Delays in the Application of Tidal Response Methods

The efficacy and applicability of tidal response methods (TRMs) were assessed in terms of the techniques used, the, data used in the analysis, and the implementation of the methods under different conditions. The tidal efficiency (TE) and time lag (TL) methods were applied to directly measured groundwater head (GWH) values in the Motril-Salobrena coastal aquifer and compared with the same pre-filtered time series after eliminating the non-tidal signals through the continuous wavelet transform (CWT) procedure. The use of maximum and minimum groundwater peaks and sea-level peaks in combination to obtain different delay values and the effects of asymmetries in tidal fluctuations were assessed. Application of the TE method yields different D values when a complete groundwater head time series is considered, instead of the net induced tidal oscillation. Moreover, when the asymmetry of tidal oscillations is not taken into account, the application of TL may yield a higher uncertainty. In unconfined coastal aquifers, hydraulic diffusivity can be overestimated by the TE method if the non-tidal components are not removed from the measured time series of groundwater head. However, prior filtering provides better diffusivity results when the TE method is applied. The depth of the water head measurements leads to different D values when applying the TE method as a consequence of the changes in the specific storage with depth, which result from changes in pressure. The results of the application of the TL method depend on whether maximum or minimum peaks are used. Since the use of maximum peak delays can overestimate D, minimum peak delays are recommended, as they yield D values that are closer to the values obtained using the TE method.

A new high-resolution model of non-tidal atmosphere and ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL06

The release 06 (RL06) of the Gravity Recovery and Climate Experiment (GRACE) Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) product has been prepared for use as a time-variable background model in global gravity research. Available since the year 1976 with a temporal resolution of 3 hr, the product is provided in Stokes coefficients up to degree and order 180. RL06 separates tidal and non-tidal signals, and has an improved long-term consistency due to the introduction of a time-invariant reference orography in continental regions. Variance reduction tests performed with globally distributed in situ ocean bottom pressure recordings and sea-surface height anomalies from Jason-2 over a range of different frequency bands indicate a generally improved performance of RL06 compared to its predecessor. Orbit tests for two altimetry satellites remain inconclusive, but GRACE K-band residuals are reduced by 0.031 nm s−2 in a global average, and by more than 0.5 nm s−2 at numerous places along the Siberian shelf when applying the latest AOD1B release. We therefore recommend AOD1B RL06 for any upcoming satellite gravimetry reprocessing effort.

Validating satellite altimeter measurements of internal tides with long‐term TAO/TRITON buoy observations at 2°S–156°E

AbstractSatellite altimetry is regularly used to map the global distribution of mode‐1 internal tides. Validating altimeter measurements of internal tides with in situ data is difficult as the mooring observations typically are too short compared with the altimetry. Here taking advantage of the long‐term (since 1999) Tropical Atmosphere‐Ocean/Triangle Trans‐Ocean Buoy Network (TAO/TRITON) buoy observations at 2°S–156°E located at a TOPEX/Poseidon crossover in a region of strong internal tides, direct comparisons are made between altimeter and in situ measurements over a common 15 year period. The hourly buoy data are decimated every 9.9 day to emulate altimeter measurements. The altimeter and decimated buoy data are highly coherent at the aliased semidiurnal period (~60 day), and they agree well for the stationary semidiurnal internal tide. For the nonstationary internal tide, which consists of a significant annual cycle, the demodulated amplitude from the altimeter appears to be contaminated by nontidal signals. The demodulated amplitude from the decimated buoy data, on the other hand, is capable of resolving the temporal variability. This suggests the potential of mapping nonstationary internal tides from satellites.

Tidal and non-tidal signals in groundwater boreholes in the KTB area, Germany

Tides and barometric pressure variations cause pore pressure changes in the solid earth. In boreholes which are hydraulically connected to confined aquifers these pore pressure changes can be observed as water level variations. In case of confined aquifers boreholes can be regarded as volumetric strainmeters. From June 2004 until May 2005 a large scale injection experiment was realised in the pilot borehole (4000 m) at the German Continental Deep Drilling (KTB) site in Bavaria. During this test the injection induced deformation was observed by a tiltmeter array around KTB consisting of five tiltmeter stations at horizontal distances from 1.6 to 3 km from the injection borehole. At each station the local groundwater level was observed in depths between 30 and 50 m. The pore pressure was recorded in the boreholes. The time series were checked for tidal signals and injection influence. The injection was not verified presumably due to the fact that the penetration of the injected water was controlled by local geology and tectonic faults zones. Although the boreholes extending only to shallow depth tidal signals are clearly observable in at least two of five stations. On December the 26th 2004 the Sumatra–Andaman earthquake occurred which is clearly detectable in the pore pressure variations at all five stations.

Sea level variability and the ‘ Milghuba’ seiche oscillations in the northern coast of Malta, Central Mediterranean

The characteristics of the water level variations in the northern coastal area of Malta are studied by a set of densely sampled data collected in the period 1993–1996 (43 months) at a permanent coastal sea level installation in Mellieha Bay. These measurements constitute the first digitised sea level recordings in the Maltese Islands and were collected as part of a research programme that produced a long time series of simultaneous water level and meteorological parameters in the Central Mediterranean. Tidal oscillations reach a maximum range of only 20.6 cm on average and are predominantly semi-diurnal. Important non-tidal signals are however found to span the whole spectral range of frequencies. Seiche oscillations in the form of large amplitude sea level fluctuations, known locally as the ‘ milghuba’, carry substantial energy in the range of long wave frequencies (0.2–2 cph) and often mask completely the tidal signal. These coastal seiches are believed to be the expression of shelf scale resonances; in the numerous embayments on the northern coastline of the Maltese Islands, these seiches are greatly amplified and have associated swift alternating currents that are useful for the mixing and exchange of the water body in the embayments with the adjoining open sea areas, but can constitute a nuisance to navigation especially at harbour entrances. In the synoptic and sub-synoptic time scales, variations in atmospheric pressure associated with mesoscale meteorological phenomena produce a predominant effect on the sea level, but the response of the sea is non-isostatic and carries the signature of oceanographic conditions in the region as well as that of non-local forcing resulting from intra-basin differences. Strong seasonal non-eustatic fluctuations in the mean sea level are characterised by a high sea level in December and is typically followed by a sharp fall to a minimum in February/March. This seasonal variability is a manifestation of the adjustments in the mass balance of the whole Mediterranean basin.

Observing long-term FCR variation using Esashi extensometers

Long duration precise and stable tidal observations are recorded to detect the temporal variation of free core nutation (also called the fluid core resonance, FCR) parameters, so as to reveal geophysical and dynamical processes at the core mantle boundary (CMB) of the Earth. At Esashi Earth Tides Station of National Astronomical Observatory of Japan, the tidal admittance and the non-tidal signal are estimated from 17 years of records with three extensometer data. From the estimated admittances of diurnal tidal constituents, the FCR parameters are fitted. The obtained time series of FCR eigenperiod and quality factor show 10–11 years scale temporal variation. The range of the eigenperiod variation is several dozens sidereal days (s.d.). This phenomenon is validated and confirmed by the gravitational tidal observation of a co-located super-conducting gravimeter (SG) with the observation from 1992 to 2002. Overestimated atmospheric response, extra loading effects from the temporal variations of local rock properties and of ocean tidal constituents, as well as the flattening variation of the topography at CMB are suggested to be the possible mechanisms to cause the periodical variation of FCR parameters.

Study of harmonic site position variations determined by very long baseline interferometry

Position variations of 40 very long baseline interferometry (VLBI) stations at 32 tidal frequencies were obtained from analysis of 3 million measurements of group delays from 1980 to 2002. Residual displacements after the removal of the effect of solid Earth tides were studied. The purpose of this study is to investigate a harmonic signal at any frequency where it is expected and to assess quantitatively whether the models of vertical and horizontal site position variations agree with the observations. It was found that the estimates of station displacements are generally in good agreement with the ocean loading computed on the basis of ocean tide models for the main diurnal and semidiurnal tides. Moreover, VLBI results allow us to discriminate between different ocean tide models. However, discrepancies between VLBI results and all models of ocean loading for K1, K2, and S2 tides exceed both the errors of the VLBI estimates and the errors of ocean loading displacements based on the reported formal uncertainties of ocean tide models. It was found that there is a significant nontidal signal at diurnal and annual frequencies. Applying a model of hydrological loading reduces the variance of the residual vertical displacements at the annual frequency by 30%. Using an empirical model of harmonic site position variations in VLBI processing provides a better fit and improves the baseline length repeatability.

Tidal and Subtidal Flow along a Cross-Shelf Transect on the East China Sea

Fourteen repetitions of a cross-shelf transect in the Kuroshio current edge in the East China Sea allowed the description of a) the semidiurnal tidal properties of the transect and b) the subduction of low salinity water at the edge of a Kuroshio meander intrusion onto the shelf. Water velocity and density profiles were obtained along the transect throughout a seven-day period of May 2000 in which warm Kuroshio waters moved onto the shelf at typical speeds of 0.1 to 0.2 m/s. Irregular lengths of the transect (maximum of ≈75 km) and the non-uniform frequency of sampling permitted elucidation only of the semidiurnal contributions to the tidal currents. The semidiurnal tidal currents in the transect exhibited typical amplitudes of 0.5 m/s, decreasing offshore. Locally, the tidal current amplitudes decreased and for the most part rotated clockwise with depth. Orientation of the tidal currents was essentially in the NW-SE direction throughout the transect and the tidal phase progressed onshore. This information contributes to the scarce observational evidence on the tidal properties of the East China Sea's continental shelf. A Kuroshio meander was identified by the gradual increase of Sea Surface Temperatures on the outer shelf of the East China Sea during the period of observation. The meander exhibited strong vertical shears and flow convergences that allowed subduction of low salinity waters at its edge. Ageostrophic traits in the meander were denoted by the development of a) cross-shelf flows and b) marked discrepancies between geostrophically derived along-shelf flow estimates and detided along-shelf flows. Similarities between geostrophic estimates and detided along-shelf flows during the first two days of observations provide confidence in the effective separation of tidal and non-tidal signals with the method employed.

High‐frequency variations in Earth rotation from Global Positioning System data

Using the data of the global, dense Global Positioning System (GPS) network established by the International GPS Service a continuous, uninterrupted series of subdaily Earth rotation parameters (ERPs) with a time resolution of 2 hours has been generated at the Center for Orbit Determination in Europe. The series starts in January 1995 and has a length of more than 3 years. Starting from the 2‐hour ERP values of this, to our knowledge, unique time series, the high‐frequency variations in Universal Time (UT1) and polar motion (PM) due to ocean tides are studied and a set of sine and cosine coefficients is estimated for all the major tidal terms at nearly diurnal and semidiurnal frequencies. The GPS series is not very homogeneous (various processing changes during the 3 years) and still short compared to the length of very long baseline interferometry (VLBI) and satellite laser ranging (SLR) data sets. However, the results derived from this series are already of the same quality as the results from VLBI and SLR. A comparison of the tidal coefficients stemming from all three space‐geodetic techniques shows an agreement on the 1 μs level for UT1 and 10 microarc seconds (μas) for PM, respectively. The RMS difference between the ocean tide amplitudes estimated from GPS data and from TOPEX/Poseidon altimeter data amounts to 0.7–0.9 μs in UT1 and 9–13 μas in PM. The residual spectrum that remains after the removal of all tidal terms has a noise level of ∼5–10 μas in PM and 0.5–1 μs in UT1 and contains nontidal signals (up to 55 μas in PM and 3 μs in UT1) that might be due to the impact of the satellite orbit modeling (12‐hour revolution period of the satellites) or, alternatively, due to atmospheric or oceanic normal modes.

The response method applied to the analysis of superconducting gravimeter data

The response method, a technique used in ocean tide analysis to separate linear and nonlinear components, is applied to the analysis of superconducting gravimeter data. A response analysis is shown to be capable of resolving small non-tidal signals of a few nanogal amplitude arbitrarily close in frequency to large amplitude tidal signals. A synthetic example, in which a small signal is injected into a spectrally rich tidal signal is used to demonstrate how the method is applied and its advantages compared to a conventional analysis. The technique is also applied to the analysis of degree 3 diurnal and semi-diurnal tides in short records. The degree 3 waves are easily separated and a reasonable ocean loading effect for these waves is recovered, despite the fact the open ocean tide is only a few mm in amplitude. Finally, a response analysis is used to separate gravitational tides from the radiation tides at coincident frequencies in both the diurnal and semi-diurnal bands.

A comparison of methods for analysis of tidal records containing multi-scale non-tidal background energy

Many tidal phenomena, including river tides, estuarine currents, and shelf and fjord internal tides, are non-stationary. These tidal processes are poorly understood and largely beyond the realm of practical prediction, even when the perturbing phenomenon causing the non-stationary behavior is itself fairly predictable. Our inadequate understanding of these phenomena has been exacerbated by an absence of a self-consistent procedure for analysis of the entire spectrum of non-stationary motions, tidal and non-tidal. The most difficult methodological situation occurs when the disturbing non-tidal signal is stronger than the tidal one and has an event-like character. Such sharp changes in forcing are multi-scale, containing energy at tidal frequencies, as well as at larger sales. Because of the distinct response of different parts of the tidal spectrum to non-tidal perturbations, multi-scale forcing events have the potential to provide a valuable new generation of tests of tidal dynamics models. This paper compares three techniques for the analysis of such signals, using artificial tidal records of known frequency content to ascertain which method most accurately represents evolving frequency content. The methods are: (a) conventional least-squares, short-term harmonic analysis (STHA); (b) a modified STHA (or mSTHA) that uses a smoothing window and augments the frequency structure of the analysis wave; and (c) linear convolution analysis in the form of continuous wavelet transforms (CWT). Results show that STHA and mSTHA lack a definable frequency response and mix energy between tidal and non-tidal signals in an unpredictable manner. STHA also effectively imposes a boxcar window on the data, the effects of which can be serve for short records. In general, STHA and mSTHA results using short windows will be least reliable in the circumstances where short windows are most desired—when the signal is highly non-stationary. There is, moreover, no simple way to set a minimum window length for STHA/mSTHA that will produce stable results, except to make the window too long to capture the fluctuating variance being sought. In contrast, CWT correctly recovers both tidal and non-tidal variance, as long as resolution limits set by the Heisenberg uncertainty principle are respected. Whatever method is chosen, use of window lengths less than ∼4–6 d requires great care, unless diurnal and subtidal energy are insignificant.

Changing mean sea level and tidal constants on the west coast of Australia

Long time-series of sea-level observations spanning 21 years (1966-86) from four ports on the west coast of Australia are analysed in yearly sets to study the secular trends and periodic changes in the tidal harmonic constituents. Mean sea level and five harmonic consistuents-Sa from low frequency band, O1 and K1 from the diurnal band, M2 and S2 from the semi-diurnal band-are investigated for secular trend and other variations that are not accounted for by conventional methods. Secular trends at Darwin, Wyndham and Geraldton are such that the amplitudes of M2 and S2 tides are decreasing and their phases are retarding. The changes observed at Fremantle are similar in magnitude but opposite in sign. In the diurnal band, variations in the phases of 01 and K1 are similar to those of the M2 and S2 tides. The observed trends of the diurnal and semidiurnal tides of Wyndham and Fremantle are well above standard error. Secular changes in the annual tide are not significant. In addition to the secular trends, these constituents are also modulated by terms which are not present in the tide-generating potential and they cannot be resolved from observations of less than 18.61 years. For example, in the spectrum of the equilibrium tide, there is no nodal term associated with the S2 constituent because it is of the solar origin, whereas in the observed tide two nodal terms appear as side bands. At some ports the amplitudes of the new nodal terms are large enough to modulate the principal tide by 2%. The mean sea level has been rising at the average rate of 1.73 mm year-1 over this period. It is modulated by a tidal signal of 18.61 years' cycle and non-tidal signals which are spatially consistent but aperiodic. A strong correlation between the residual component of the annual mean sea level and Southern Oscillation Index suggests that non-tidal long-period perturbations of mean sea level (MSL) are mainly due to El Nino-Southern Oscillation effects.