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1. An Assessment of Global Ocean Barotropic Tide Models Using Geodetic Mission Altimetry and Surface Drifters

   https://doi.org/10.1175/JPO-D-20-0089.1  

   Zaron, Edward D.; Elipot, Shane (January 2021, Journal of Physical Oceanography)

   null (Ed.)

   Abstract The accuracy of three data-constrained barotropic ocean tide models is assessed by comparison with data from geodetic mission altimetry and ocean surface drifters, data sources chosen for their independence from the observational data used to develop the tide models. Because these data sources do not provide conventional time series at single locations suitable for harmonic analysis, model performance is evaluated using variance reduction statistics. The results distinguish between shallow and deep-water evaluations of the GOT410, TPXO9A, and FES2014 models; however, a hallmark of the comparisons is strong geographic variability that is not well summarized by global performance statistics. The models exhibit significant regionally coherent differences in performance that should be considered when choosing a model for a particular application. Quantitatively, the differences in explained SSH variance between the models in shallow water are only 1%–2% of the root-mean-square (RMS) tidal signal of about 50 cm, but the differences are larger at high latitudes, more than 10% of 30-cm RMS. Differences with respect to tidal currents variance are strongly influenced by small scales in shallow water and are not well represented by global averages; therefore, maps of model differences are provided. In deep water, the performance of the models is practically indistinguishable from one another using the present data. The foregoing statements apply to the eight dominant astronomical tides M 2 , S 2 , N 2 , K 2 , K 1 , O 1 , P 1 , and Q 1 . Variance reduction statistics for smaller tides are generally not accurate enough to differentiate the models’ performance. 

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2. A new-generation internal tide model based on 30 years of satellite sea surface height measurements: multiwave decomposition and isolated beams

   https://doi.org/10.5194/essd-17-3949-2025  

   Zhao, Zhongxiang (August 2025, Earth System Science Data)

   An internal tide model, ZHAO30yr, is developed using 30 years of satellite altimetry sea surface height (SSH) measurements from 1993 to 2022 by a recently improved mapping technique that consists of two rounds of plane wave analysis with a spatial bandpass filter in between. Prerequisite wavelengths are calculated using climatological annual mean hydrographic profiles in the World Ocean Atlas 2018. ZHAO30yr only extracts the 30-year phase-locked internal tide component, lacking the incoherent component caused by the time-varying ocean environment. The model contains 12 internal tide constituents: eight mode-1 constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) and four mode-2 constituents (M2, S2, K1, and O1). Model errors are estimated to be lower than 1 mm in the SSH amplitude on global average, thanks to the long data record and improved mapping technique. The model is evaluated by making internal tide correction to independent altimetry data for 2023. A total of 10 constituents (but for K2 and Q1) can reduce variance on global average. K2 and Q1 can only cause variance reductions in their source regions. The model decomposes the multiconstituent, multimodal, multidirectional internal tide field into a series of simple plane waves at each grid point. The decomposition reveals unprecedented features previously masked by multiwave interference. The model divides each internal tide constituent into components by propagation direction. The directionally decomposed components show numerous long-range internal tidal beams associated with notable topographic features. The semidiurnal internal tidal beams off the Amazon shelf and the diurnal internal tidal beams in the Arabian Sea are examined in detail. ZHAO30yr is available at https://doi.org/10.6084/m9.figshare.28078523 (Zhao, 2024b). Model errors are available at https://doi.org/10.6084/m9.figshare.28559978.v3 (Zhao, 2025). 

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3. Optimal Frequency-domain Analysis for Spacecraft Time Series: Introducing the Missing-data Multitaper Power Spectrum Estimator

   https://doi.org/10.3847/1538-3881/ad0c58  

   Dodson-Robinson, Sarah; Haley, Charlotte (December 2023, The Astronomical Journal)

   Abstract While the Lomb–Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60 yr history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. TheF-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise–based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper–F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex “scallop-shell” shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence. 

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4. Detecting Instantaneous Tidal Signals in Ocean Models Utilizing Streaming Band‐Pass Filters

   https://doi.org/10.1029/2024MS004319  

   Xu, Chengzhu; Zaron, Edward D (October 2024, Journal of Advances in Modeling Earth Systems)

   Abstract Through the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting. 

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5. Graph Learning From Multivariate Dependent Time Series Via A Multi-Attribute Formulation

   https://doi.org/10.1109/ICASSP43922.2022.9746603  

   Tugnait, Jitendra K. (May 2022, ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges. 

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