Investigation of bias in traditional grouping by means of regularization

<p>Harmonic tidal analysis bases on the presumption that since short records and close frequencies result in an ill-conditioned matrix equation, a record of length T is required to distinguish harmonics with a frequency separation of 1/T (Rayleigh criterion). To achieve stability of the solution, tidal harmonics are grouped. Nevertheless, if any additional information from different harmonics within the assumed groups is present in the data, it cannot be resolved. While the most information in each group is carried by the harmonic with the largest amplitude, time series from other harmonics is properly taken into account in estimated amplitudes and phases. However, if the signal from the next largest harmonic in a group is significantly different from the expectation, the grouping parametrization might lead to an inaccurate estimate of tidal parameters. That might be an issue since harmonics in a group do not have the same admittance factor, or if the assumed relationship between harmonics degree 2 and 3 is false.</p><p>The bias caused by grouping tidal harmonics can be investigated with methods used for stabilizing inverse problem solutions. In our study, we abandon the concept of groups. The resulting ill-posedness of the problem is reduced by constraining the model parameters (1) to reference values and (2) to the condition that admittance shall be a smooth function of frequency. The mentioned regularization terms are present in the least-squares objective function, and the trade-off parameter between the model misfit and data residuals is chosen by the L-curve criterion. We demonstrate how this method may be used to reveal system properties hidden by wave grouping in tidal analysis. We also suggest that forcing time series amplitude may be more relevant grouping criterion than solely frequency closeness of harmonics.</p>

Variations in physiography, tidal forcing, and bottom shear stress in palaeo-seas: lessons learned from numerical modelling.

<p>The physiography (geometry and bathymetry) of a basin and its latitude are the primary parameters that dictate the tidal dynamics in shoreline–shelf systems. Understanding the impact that changes in physiography have on tides allows researchers to 1) improve interpretations of historical sedimentary processes in shallow-marine basins, and 2) better predict potential variations in tidal dynamics in response to an anthropogenic-driven relative sea level change.</p><p>Here, we present an analysis of numerical modelling of tidal propagation in the Upper Jurassic Sundance and Curtis Seas demontrating that basin-scale amplification and dampening of tides occurred in different palaeophysiographic configurations, and more localised amplification relating to tidal harmonics occurred in certain physiographic scenarios. Consequently, palaeophysiography was the primary control on both the magnitude and location of tidal amplification, flow speed, and bed shear stress, whereas secondary controls were initial tidal forcing and bottom drag coefficient.</p><p>Simulation results for the palaeophysiography with a 600 m depth at the mouth of the system suggest a distribution of sedimentary facies comparable to those documented in the Upper Jurassic lower Curtis Formation, apart from the innermost Curtis Sea, near to the palaeoshoreline. Sediments potentially supplied by aeolian processes during regression and increased aridity were likely reworked by tides during a subsequent a transgression as the climate became more humid. The palaeophysiography with a 600 m depth at the mouth of the system can therefore be considered a realistic palaeophysiographic configuration for the Sundance and Curtis Seas given the similarities that exist between the predicted distribution of sedimentary facies and their actual distribution in the lower Curtis Formation. In this palaeophysiography, the Sundance Sea and the Curtis Sea would have thus attained a maximum depth of ~240 m and 40-45 m, respectively. In this context, the simulated tidal range in the Curtis Sea would have reached 2.60 m, which would classify the Curtis Sea as a meso-tidal system (2x 1.30 m tidal amplitude).</p><p>Finally, using change in palaeophysiographic configuration as a proxy for relative sea-level variations revealed the non-uniqueness (sensu Burgess & Prince, 2015) of sedimentary successions deposited in tide-dominated basin, given that tidal amplification in the system was controlled by palaeophysiographic configuration: one specific succession could be the product of several, equally-valid relative sea-level histories. Reciprocally, the impact of relative sea-level change on different successions is non-unique, since local tidal harmonics and the characteristics of coeval deposition may vary significantly during relative sea level changes.</p>

A comparison of predicted and observed ocean tidal loading in Alaska

SUMMARY We investigate the elastic and anelastic response of the crust and upper mantle across Alaska to mass loading by ocean tides. GPS-inferred surface displacements recorded by the Plate Boundary Observatory network are compared with predictions of deformation associated with the redistribution of ocean water due to the tides. We process more than 5 yr of GPS data from 131 stations using a kinematic precise point positioning algorithm and estimate tidal contributions using harmonic analysis. We also forward calculate load-induced surface displacements by convolving ocean-tide models with load Green’s functions derived from spherically symmetric Earth models. We make the comparisons for dominant tidal harmonics in three frequency bands: semidiurnal (M2), diurnal (O1) and fortnightly (Mf). Vector differences between predicted and observed ocean tidal loading (OTL) displacements are predominantly sub-mm in magnitude in all three frequency bands and spatial components across the network, with larger residuals of up to several mm in some coastal areas. Accounting for the effects of anelastic dispersion in the upper mantle using estimates of Q from standard Earth models reduces the residuals for the M2 harmonic by an average of 0.1–0.2 mm across the network and by more than 1 mm at some individual stations. For the relatively small Mf tide, the effects of anelastic dispersion (<0.03 mm) are undetectable within current measurement error. Incorporating a local ocean-tide model for the northeastern Pacific Ocean reduces the M2 vertical residuals by an average of 0.2 mm, with improvements of up to 5 mm at some coastal stations. Estimated RMS observational uncertainties in the vertical component for the M2 and O1 tides are approximately ±0.08 mm at the two-sigma level (±0.03 mm in the horizontal components), and ±0.21 mm for the Mf harmonic (±0.07 mm in the horizontal components). For the M2 harmonic, discrepancies between predicted and observed OTL displacements exceed observational uncertainties by about one order of magnitude. None of the ocean tide and Earth model combinations is found to reduce the M2 residuals below the observational uncertainty, and no single forward model provides a best fit to the observed displacements across all tidal harmonics and spatial components. For the O1 harmonic, discrepancies between predicted and observed displacements are generally several-fold larger than the observational uncertainties. For the Mf harmonic, the discrepancies are roughly within a factor of two of the observational uncertainties. We find that discrepancies between predicted and observed OTL displacements can be significantly reduced by removing a network-uniform tidal-harmonic displacement, and that the remaining discrepancies exhibit some regional-scale spatial coherency, particularly for the M2 harmonic. We suggest that the remaining discrepancies for the M2, O1 and Mf tides cannot be fully explained by measurement error and instead convey information about deficiencies in ocean-tide models and deviations from spherically symmetric Earth structure.

Providential Tides: the Double Low Water of Narragansett Bay

We investigate a mechanism for producing double-lows and double-highs in the semi-diurnal tide by selective amplification of higher harmonics in a resonant gulf. A double low water is observed at Providence, RI, near the head of Narragansett Bay on days when there is a flattening of the low water tidal curve at Newport, at the mouth of the bay. The flattening is caused by an unusually large quarter-diurnal component to the tide at Newport. The quarter diurnal component has the right phase (a maximum close to the time of the minimum in the semi-diurnal tide) to produce a prolonged flattening of the tidal curve around low water. The natural period of Narragansett Bay (for quarter-wavelength resonance) is close to 4 h and the quarter diurnal tide is amplified, relative to the semi-diurnal tide, within the bay. The selective amplification of the higher harmonic further prolongs the flattening effect at Providence and, occasionally, is sufficient to create a double low water at the head of the bay from quarter and semi-diurnal tides alone. More often, though, a sixth-diurnal harmonic produced within the bay, added to the flattened low water at Providence, creates the double low water. This mechanism of selective amplification of tidal harmonics could be relevant to double tides elsewhere.

Resolution and significant contributions of tidal forcing in flexible harmonic grouping computed using Singular Value Decomposition

<p>We present the results of our studies of singular value decomposition (SVD) of the forward operator in tidal analysis. Using the resolution matrix and the ratio between singular values, we distinguish significant contributions that compose the tidal signal and we study cross-talk within and between tidal groups. Using all harmonics from the tidal catalogue we investigate the resolution matrix properties with decreasing amplitude of harmonics. We demonstrate the loss of resolution even for harmonics of large amplitude with decreasing time-series length. Our further investigation shows the cross-talk from atmospherically induced gravity variation into a tidal signal (expected and unexpected, e.g. S1, Fi1, Sig1). We investigate the ability to determine the ratio of gravimetric factors of degree 2 and degree 3 tides from the specific tidal gravity signal recordings.</p><p><span>The main interest of tidal analysis is the accurate and precise determination of tidal parameters, which are amplitude (gravimetric) factor and phase lag, the quantities describing the Earth response to the tidal forcing. Tidal catalogues </span><span>define the tide generating potential in terms </span><span>of harmonics. Widely used software, like ETERNA or Baytap-G, uses a-priori grouping of harmonics which is based on reasonable considerations like the Rayleigh criterion of spectral resolution. Wave grouping is a model parameteri</span><span>s</span><span>ation used to make the analysis problem overdetermined by using assumptions regarding the model parameters (e.g. credo of smoothness, known free-core resonance parameters, known ratio between response to degree 2 and degree 3 forcing). </span><span>If</span><span> those assumptions are incorrect, this can lead to artefacts which might go unnoticed. This presents a limitation for example in the search for causes of temporal variation of tidal parameters, as reported recently. SVD of the unparameterised problem allows us to investigate these limitations.</span></p><p><span>In our analysis, SVD is a factorisation of a linear regression matrix. The regression matrix consists of tidal harmonics in-phase and quadrature signal for rigid Earth tide (tidal forcing to Earth surface). We compute time series for each harmonic present in Tamura tidal catalogue </span><span>by </span><span>using a modified version of "Predict" (ETERNA package). Resulting values can be, but do not need </span><span>to</span><span> be, grouped prior to SVD analysis. Other than with conventional programs, wave groups can not only be defined along the frequency axis. They can as well be used to separate harmonics of degree 2 and degree 3. SVD allows us to study the significance of tidal harmonics, cross-talk between harmonics or groups and matrix null space. Thus, we can discriminate the parameters with small singular value, which do not significantly contribute to the predicted tidal data or are noise-sensitive.</span></p>

Variations of upper atmospheric high-order solar tidal harmonics during sudden stratospheric warming 2018

<p>Solar tides are the most predictably-occurring waves in the upper atmosphere. Although the dynamical theory can be dated back to Laplace in the 16th century, in the upper atmosphere tides  were rarely studied observationally until satellites and ground-based radars became common. To date, studies have mainly focused on low-order harmonics. Here, we combine mesospheric wind observations from three longitudinal sectors to investigate high-order harmonics. Results illustrate that the first six harmonics appear in early 2018, all of which are dominated by sum-synchronous components. Among these harmonics, the 6hr, 4.8hr, and 4hr components weaken at the sudden stratospheric warming (SSW) onset. The weakening could be explained in terms of variations in the background zonal wind.</p>

ANALISIS PASANG SURUT MENGGUNAKAN METODE LEAST SQUARE DI WILAYAH PERAIRAN ENDE, NUSA TENGGARA TIMUR

Abstrak Telah dilakukan penelitian tentang analisis pasang surut menggunakan metode Least Square di wilayah perairan Ende, Nusa Tenggara Timur. Penelitian ini bertujuan untuk menentukan komponen harmonik pasang surut menggunakan metode Least Square serta menganalisis tipe pasang surut menggunakan bilangan Formzahl. Berdasarkan hasil analisis data, diketahui bahwa komponen pasang surut yaitu M2, S2, N2, K1, O1, Q1 dan tipe pasang surut di perairan Ende termasuk tipe campuran condong keharian ganda (mixed tide prevailing semidiurnal) dengan nilai Formzhal (F) setiap bulannya adalah (0,38), (0,31), (0,25), (0,28), (0,38), (0,44), (0,41), (0,33), (0,25), (0,27) (0,35) dan 0,42. Hasil analisis pasang surut menunjukkan nilai amplitudo harmonik pasang surut ganda utama M2 dan S2 lebih dominan dibandingkan komponen pasang surut tunggal utama K1 dan O1. Kata Kunci: Least Square, Campuran Condong Harian Ganda, Perairan Ende. Abstract Research on tidal analysis has been done using the Least Square method in the sea area surrounding Ende, East Nusa Tenggara. This research aims to determine the components of tidal harmonics using the Least Square method and to analyze the type of tides using Formzhal number. Based on the results of analysis data, it is known that tidal harmonic components are M2, S2, N2, K1, O1, Q1 and the type of tides in Ende sea included mixed type of tide prevailing semidiurnal with Formzhal (F) value of (0.38), (0.31), (0.25), (0.28), (0.38), (0.44), (0.41), (0.33), (0.25), (0.27), (0.35), and 0.42. The results show the amplitude of the main tidal component M2 and S2 is the dominant component in the Ende Sea compared to the main single tidal component K1 and O1. Keywords: Least Square, Mixed Tide Prevailing Semidiurnal, Ende Sea.

Using barometric time series of the IMS infrasound network for a global analysis of thermally induced atmospheric tides

The International Monitoring System (IMS) has been established to monitor compliance with the Comprehensive Nuclear-Test-Ban Treaty and comprises four technologies, one of which is infrasound. When fully established, the IMS infrasound network consists of 60 sites uniformly distributed around the globe. Besides its primary purpose of determining explosions in the atmosphere, the recorded data reveal information on other anthropogenic and natural infrasound sources. Furthermore, the almost continuous multi-year recordings of differential and absolute air pressure allow for analysing the atmospheric conditions. In this paper, spectral analysis tools are applied to derive atmospheric dynamics from barometric time series. Based on the solar atmospheric tides, a methodology for performing geographic and temporal variability analyses is presented, which is supposed to serve for upcoming studies related to atmospheric dynamics. The surplus value of using the IMS infrasound network data for such purposes is demonstrated by comparing the findings on the thermal tides with previous studies and the Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2), which represents the solar tides well in its surface pressure fields. Absolute air pressure recordings reveal geographical characteristics of atmospheric tides related to the solar day and even to the lunar day. We therefore claim the chosen methodology of using the IMS infrasound network to be applicable for global and temporal studies on specific atmospheric dynamics. Given the accuracy and high temporal resolution of the barometric data from the IMS infrasound network, interactions with gravity waves and planetary waves can be examined in future for refining the knowledge of atmospheric dynamics, e.g. the origin of tidal harmonics up to 9 cycles per day as found in the barometric data sets. Data assimilation in empirical models of solar tides would be a valuable application of the IMS infrasound data.

Using barometric time series of the IMS infrasound network for a global analysis of thermally induced atmospheric tides

The International Monitoring System (IMS) has been established to monitor compliance with the Comprehensive Nuclear-Test-Ban Treaty and comprises four technologies, one of which is infrasound. When fully established, the IMS infrasound network consists of 60 sites homogeneously distributed around the globe. Besides its primary purpose of determining explosions in the atmosphere, the recorded data reveal information on other anthropogenic and natural infrasound sources. Furthermore, the almost continuous multiyear recordings of differential and absolute air pressure allow for analysing the atmospheric conditions. In this paper, spectral analysis tools are applied to derive atmospheric dynamics from barometric time series. Based on the solar atmospheric tides, a methodology for performing geographic and temporal variability analyses is presented which is supposed to serve for upcoming studies related to atmospheric dynamics. The surplus value of using the IMS infrasound network data for such purposes is demonstrated by comparing the findings on the thermal tides with previous studies and the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2), which well represents the solar tides in its surface pressure fields. Absolute air pressure recordings reveal geographic characteristics of atmospheric tides related to the solar day and even to the lunar day. We therefore claim the chosen methodology of using the IMS infrasound network to be applicable for global and temporal studies on specific atmospheric dynamics. Given the accuracy and high temporal resolution of the barometric data from the IMS infrasound network, interactions with gravity waves and planetary waves can be examined in future for refining the knowledge of atmospheric dynamics; e.g., the origin of tidal harmonics up to 9 cycles per day as found in the barometric data sets. Data assimilation in empirical models of solar tides would be a valuable application of the IMS infrasound data.