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Dynamic and Regression Modeling of Ocean Variability in the Tide-Gauge Record at Seasonal and Longer Periods

Comparison of monthly mean tide-gauge time series to corresponding model time series based on a static inverted barometer (IB) for pressure-driven fluctuations and a ocean general circulation model (OM) reveals that the combined model successfully reproduces seasonal and interannual changes in relative sea level at many stations. Removal of the OM and IB from the tide-gauge record produces residual time series with a mean global variance reduction of 53%. The OM is mis-scaled for certain regions, and 68% of the residual time series contain a significant seasonal variability after removal of the OM and IB from the tide-gauge data. Including OM admittance parameters and seasonal coefficients in a regression model for each station, with IB also removed, produces residual time series with mean global variance reduction of 71%. Examination of the regional improvement in variance caused by scaling the OM, including seasonal terms, or both, indicates weakness in the model at predicting sea-level variation for constricted ocean regions. The model is particularly effective at reproducing sea-level variation for stations in North America, Europe, and Japan. The RMS residual for many stations in these areas is 25-35 mm. The production of "cleaner" tide-gauge time series, with oceanographic variability removed, is important for future analysis of nonsecular and regionally differing sea-level variations. Understanding the ocean model's strengths and weaknesses will allow for future improvements of the model.

Hill, Emma M.↗

Tidal simulation using regional ocean modeling systems (ROMS)

The purpose of our research is to test the capability of ROMS in simulating tides. The research also serves as a necessary exercise to implement tides in an operational ocean forecasting system. In this paper, we emphasize the validation of the model tide simulation. The characteristics and energetics of tides of the region will be reported in separate publications.

tide modeling↗

Model simulations of Plum Island Ecosystems LTER low marsh site using ELM-PFLOTRAN

Model simulations using the E3SM Land Model (ELM) coupled to the PFLOTRAN reactive transport model via the Alquimia interface. The simulations were conducted for a tidal salt marsh at the Plum Island Ecosystems LTER near Rowley, Massachusetts, USA. Model simulations were forced using site-specific tidal cycles and salinity, and the simulations used a biogeochemical reaction network including aerobic decomposition, sulfate reduction, iron reduction, and methanogenesis. Model outputs include simulated carbon stocks, carbon dioxide and methane fluxes, and porewater concentrations of key solutes related to sulfur, iron, and carbon cycling. The model simulations included a saline simulation (with tidal sulfate inputs), a fresh simulation (with low salinity and low sulfate inputs), and a saline simulation with lower vegetation productivity to represent the effect of salinity on vegetation. These simulations were conducted to demonstrate that a new model framework incorporating subsurface redox and biogeochemical interactions into a land surface model could reproduce measured surface greenhouse gas fluxes and biogeochemical dynamics in tidal marsh ecosystems, and to test whether including redox interactions in a land surface model would allow the model to resolve contrasts in biogeochemical cycling and greenhouse gas production between saline and freshwater wetlands.The data package includes gzipped tar archives (which can be expanded using standard tar and gzip utilities) of model outputs from three model configurations: saline subsurface and reduced vegetation productivity related to salinity; saline subsurface with vegetation productivity not reduced; and freshwater. Also included are code for the modified E3SM model, Alquimia interface, and PFLOTRAN reactive transport simulator in gzipped tar format; plain text parameter and configuration files; python code files for visualizing model output and defining model configurations; and model output, tide and salinity forcing, and configuration files in netCDF format. See the README.md file in the data package for a detailed description of all files contained in the package. All files are in netCDF (.nc), gzipped tar archive (.tar.gz or .tgz), or text (all other files).Updated: May 13, 2024. Model output, E3SM code, PFLOTRAN input files, and python codes for visualizing results were updated to reflect changes made for the manuscript revision. The updated archive reflects the code and model output from the final accepted manuscript. Changes included updated reaction parameters reflecting improved parameterization and additional comparisons with field measurements. E3SM code changes included better support for multiple grid cells and improved flow and transport parameterization.

54 ENVIRONMENTAL SCIENCES↗

Ocean-Science Mission Needs: Real-Time AUV Data for Command, Control, and Model Inputs

Predictive models for tides, hydrodynamics, and bio-optical properties affecting the visibility and buoyancy of coastal waters are needed to evaluate the safety of personnel and equipment engaged in maritime operations under potentially hazardous conditions. Predicted currents can be markedly different for two-layer systems affected by terrestrial runoff than for well-mixed conditions because the layering decouples the surface and bottom Ekman layers and rectifies the current response to oscillatory upwelling-and downwelling-favorable winds. Standard ocean models (e.g. Princeton Ocean Model) require initial-and boundary data on the physical and optical properties of the multilayered water column to provide accurate simulations of heat budgets and circulation. Two observational systems are designed to measure vertically structured conditions on the West Florida Shelf (WFS): a tethered buoy network and an autonomous underwater vehicle (AUV) observational system. The AUV system is described with a focus on the observational systems that challenge or limit the communications command and control network for various types of measurement programs. These include vertical oscillatory missions on shelf transects to observe the optical and hydrographic properties of the water column, and bottom-following missions for measuring the bottom albedo. Models of light propagation, absorption, and conversion to heat as well as determination of the buoyancy terms for physical models require these measurements. High data rates associated with video bottom imagery are the most challenging for the real-time, command and control communications system, but they are met through a combination of loss-less and lossy data-compression methods, depending upon the data-rate of the radio links.

Carder, Kendall L.↗

Uncertainty-Guided Prediction Horizon of Phase-Resolved Ocean Wave Forecasting Under Data Sparsity: Experimental and Numerical Evaluation

Accurate short-term wave forecasting is critical for the safe and efficient operation of marine structures that rely on real-time, phase-resolved ocean wave information for control and monitoring purposes (e.g., digital twins). These systems often depend on environmental sensors (e.g., waverider buoys, wave-sensing LIDAR). Challenges arise when upstream sensor data are missing, sparse, or phase-shifted due to drift. This study investigates the performance of two machine learning models, time-series dense encoder (TiDE) and long short-term memory (LSTM), for forecasting phase-resolved ocean surface elevations under varying degrees of data degradation. We introduce the τ-trimming algorithm, which adapts the prediction horizon based on uncertainty thresholds derived from historical forecasts. Numerical wave tank (NWT) and wave basin experiments are used to benchmark model performance under short- and long-term data masking, spatially coarse sensor grids, and upstream phase shifts. Results show under a 50% probability of upstream data loss, the τ-trimmed TiDE model achieves a 46% reduction in error at the most upstream target, compared to 22% for LSTM. Furthermore, phase misalignment in upstream data introduces a near-linear increase in forecast error. Under moderate model settings, a ±3 s misalignment increases the mean absolute error by approximately 0.5 m, while the same error is accumulated at ±4 s using the more conservative approach. These findings inform the design of resilient, uncertainty-aware wave forecasting systems suited for realistic offshore sensing environments.

42 ENGINEERING↗

Zonal winds near Venus' cloud top level - A model study of the interaction between the zonal mean circulation and the semidiurnal tide

The Holton (1982) wave-mean flow interaction model's primitive equation is presently adapted in order to clarify the interaction between the semidiurnal tide and the thermally driven mean meridional circulation near cloud top level. The model is found to produce midlatitude jets whose structure is insensitive to vertical shear of the background angular velocity, both above and below cloud top level; a sensitivity to background angular velocity at cloud top level, however, is noted. Agreement between the model tide and either the observed one or that generated by the more detailed calculations of Pechmann and Ingersoll (1984) is found to be greatest when the background angular velocity at the jet level is of the order of 30 percent larger than that which is observed.

Baker, Nancy L.↗

Tidal Models In A New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising.

Ray, Richard D.↗

TOPEX/POSEIDON tides estimated using a global inverse model

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Egbert, Gary D.↗

Australian tidal currents – assessment of a barotropic model (COMPAS v1.3.0 rev6631) with an unstructured grid

While the variations of tidal range are large and fairly well known across Australia (less than 1 m near Perth but more than 14 m in King Sound), the properties of the tidal currents are not. We describe a new regional model of Australian tides and assess it against a validation dataset comprising tidal height and velocity constituents at 615 tide gauge sites and 95 current meter sites. The model is a barotropic implementation of COMPAS, an unstructured-grid primitive-equation model that is forced at the open boundaries by TPXO9v1. The mean absolute error (MAE) of the modelled M2 height amplitude is 8.8 cm, or 12 % of the 73 cm mean observed amplitude. The MAE of phase (10°), however, is significant, so the M2 mean magnitude of vector error (MMVE, 18.2 cm) is significantly greater. The root sum square over the eight major constituents is 26 % of the observed amplitude. We conclude that while the model has skill at height in all regions, there is definitely room for improvement (especially at some specific locations). For the M2 major axis velocity amplitude, the MAE across the 95 current meter sites, where the observed amplitude ranges from 0.1 to 156 cm s −1 , is 6.9 cm s −1 , or 22 % of the 31.7 cm s −1 observed mean. This nationwide average result is encouraging, but it conceals a very large regional variation. Relative errors of the tidal current amplitudes on the narrow shelves of New South Wales (NSW) and Western Australia exceed 100 %, but tidal currents are weak and negligible there compared to non-tidal currents, so the tidal errors are of little practical significance. Looking nationwide, we show that the model has predictive value for much of the 79 % of Australia's shelf seas where tides are a major component of the total velocity variability. In descending order this includes the Bass Strait, the Kimberley to Arnhem Land, and southern Great Barrier Reef regions. There is limited observational evidence to confirm that the model is also valuable for currents in other regions across northern Australia. We plan to commence publishing “unofficial” tidal current predictions for chosen regions in the near future based on both our COMPAS model and the validation dataset we have assembled.

Tidal currents↗

A numerical modeling study of the interaction between the tides and the circulation forced by high-latitude plasma convection

A spectral, time-varying thermospheric general circulation model has been used to study the nonlinear interaction at high latitudes between the tides propagating into the thermosphere from below and the circulation induced by magnetospheric forcing and in situ solar heating. The model is discrete in the vertical with 27 layers spaced by half a scale height. In the horizontal, the fields are expanded in a series of spherical harmonics using a triangular truncation at wave number 31, equivalent to a homogeneous global resolution with a minimum wavelength of 1270 km. A hypothetical uniform grid point model would require a horizontal spacing of 417 km to describe the same minimum wavelength. In the high-latitude F region the tides affect the dusk vortex of the neutral flow very little, but the dawn vortex is either suppressed or amplified dependent upon the universal time and tidal phase. In the E region neutral flow, both the dusk and dawn vortices are shifted in local time by the tides, again as a function of universal time and tidal phase. At dusk a nonlinear amplification of the sunward winds occurs for certain combinations of parameters, and at dawn the winds may be completely suppressed. Below 120 km altitude the magnetospheric forcing creates a single cyclonic vortex which is also sensitive to the high-latitude tidal structure.

Mikkelsen, I. S.↗

Fortnightly Earth Rotation, Ocean Tides, and Mantle Anelasticity

Sustained accurate measurements of earth rotation are one of the prime goals of Global Geodetic Observing System (GGOS). We here concentrate on the fortnightly (Mf) tidal component of earth-rotation data to obtain new results concerning anelasticity of the mantle at this period. The study comprises three parts: (1) a new determination of the Mf component of polar motion and length-of-day from a multi-decade time series of space-geodetic data; (2) the use of the polar-motion determination as one constraint in the development of a hydrodynamic ocean model of the Mf tide; and (3) the use of these results to place new constraints on mantle anelasticity. Our model of the Mf ocean tide assimilates more than fourteen years of altimeter data from the Topex/Poseidon and Jason-1 satellites. The polar motion data, plus tide-gauge data and independent altimeter data, give useful additional information, with only the polar motion putting constraints on tidal current velocities. The resulting ocean-tide model, plus the dominant elastic body tide, leaves a small residual in observed length-of-day caused by mantle anelasticity. The inferred effective tidal 0 of the anelastic body tide is 90 and is in line with a omega-alpha frequency dependence with alpha in the range 0.2--0.3.

Ray, Richard D.↗

Research on Earth's rotation and the effect of atmospheric pressure on vertical deformation and sea level variability

The work done under NASA grant NAG5-485 included modelling the deformation of the earth caused by variations in atmospheric pressure. The amount of deformation near coasts is sensitive to the nature of the oceanic response to the pressure. The PSMSL (Permanent Service for Mean Sea Level) data suggest the response is inverted barometer at periods greater than a couple months. Green's functions were constructed to describe the perturbation of the geoid caused by atmospheric and oceanic loading and by the accompanying load-induced deformation. It was found that perturbation of up to 2 cm are possible. Ice mass balance data was used for continental glaciers to look at the glacial contributions to time-dependent changes in polar motion, the lod, the earth's gravitational field, the position of the earth's center-of-mass, and global sea level. It was found that there can be lateral, non-hydrostatic structure inside the fluid core caused by gravitational forcing from the mantle, from the inner core, or from topography at the core/mantle or inner core/outer core boundaries. The nutational and tidal response of a non-hydrostatic earth with a solid inner core was modeled. Monthly, global tide gauge data from PSMSL was used to look at the 18.6-year ocean tide, the 14-month pole tide, the oceanic response to pressure, the linear trend and inter-annual variability in the earth's gravity field, the global sea level rise, and the effects of post glacial rebound. The effects of mantle anelasticity on nutations, earth tides, and tidal variation in the lod was modeled. Results of this model can be used with Crustal Dynamics observations to look at the anelastic dissipation and dispersion at tidal periods. The effects of surface topography on various components of crustal deformation was also modeled, and numerical models were developed of post glacial rebound.

Wahr, John↗

Prescreening-Based Subset Selection for Improving Predictions of Earth System Models With Application to Regional Prediction of Red Tide

We present the ensemble method of prescreening-based subset selection to improve ensemble predictions of Earth system models (ESMs). In the prescreening step, the independent ensemble members are categorized based on their ability to reproduce physically-interpretable features of interest that are regional and problem-specific. The ensemble size is then updated by selecting the subsets that improve the performance of the ensemble prediction using decision relevant metrics. We apply the method to improve the prediction of red tide along the West Florida Shelf in the Gulf of Mexico, which affects coastal water quality and has substantial environmental and socioeconomic impacts on the State of Florida. Red tide is a common name for harmful algal blooms that occur worldwide, which result from large concentrations of aquatic microorganisms, such as dinoflagellate Karenia brevis, a toxic single celled protist. We present ensemble method for improving red tide prediction using the high resolution ESMs of the Coupled Model Intercomparison Project Phase 6 (CMIP6) and reanalysis data. The study results highlight the importance of prescreening-based subset selection with decision relevant metrics in identifying non-representative models, understanding their impact on ensemble prediction, and improving the ensemble prediction. These findings are pertinent to other regional environmental management applications and climate services. Additionally, our analysis follows the FAIR Guiding Principles for scientific data management and stewardship such that data and analysis tools are findable, accessible, interoperable, and reusable. As such, the interactive Colab notebooks developed for data analysis are annotated in the paper. This allows for efficient and transparent testing of the results’ sensitivity to different modeling assumptions. Moreover, this research serves as a starting point to build upon for red tide management, using the publicly available CMIP, Coordinated Regional Downscaling Experiment (CORDEX), and reanalysis data.

54 ENVIRONMENTAL SCIENCES↗

Modeling the Observed QBO and Inter-Annual Variations of the Diurnal Tide in the Mesosphere

In the current version of the Numerical Spectral Model (NSM), the Quasi-biennial Oscillation (QBO) is generated primarily by small-scale gravity waves (GW) from Hines' Doppler Spread Parameterization (DSP). The model does not have topography, and the planetary waves are solely generated by instabilities. We discuss a 3D modeling study that describes the QBO extending from the stratosphere into the upper mesosphere, where the oscillation produces significant inter-annual variations in the diurnal tide. The numerical results are compared with temperature measurements from the SABER (TIMED) and MLS (UARS) instruments obtained by Huang et al. (2006). With a GW source that peaks at the Equator and is taken to be isotropic and independent of season, the NSM generates a QBO with variable periods around 26 months and zonal wind amplitudes of almost 25 m/s at 30 km. As reported earlier, the NSM reproduces the observed equinoctial maxima in the diurnal tide at altitudes around 95 km. The modeled QBO modulates the tide such that the seasonal amplitude maxima can vary from one year to another by as much as 30%. To shed light on the underlying mechanisms, the relative importance of the advection terms are discussed, and they are shown to be important in the stratosphere. At altitudes above 80 km, however, the QBO-related inter-annual variations of the tide are generated primarily by GW momentum deposition. In qualitative agreement with the SABER measurements, the model generates distinct zonal-mean QBO temperature variations in the stratosphere and mesosphere. In the stratosphere, the computed amplitudes are not much smaller than those observed, and the rate of downward propagation at the Equator is reproduced. The modeled temperature amplitudes in the mesosphere, however, are much smaller than those observed. The observed and computed temperature variations of the QBO peak at the Equator but extend with phase reversals to high latitudes, in contrast to the zonal winds that are confined to equatorial latitudes. Hemispherical asymmetries also appear in both the model results and the observations. The temperature amplitudes outside the equatorial region however tend to occur at lower latitudes in the model results. While there is qualitative agreement between the TIMED measurements and the model prediction, there are some areas of significant disagreement that require us to reexamine the present version of the NSM. The numerical results critically depend on the chosen parameters that determine the wave forcing, and there are a number of avenues to improve the performance of the model that had not been tuned to fit the observations. The GW spectrum and its latitude dependence in the troposphere are not well known, and numerical experiments are discussed that describe the related model response. While it appears that eastward propagating Kelvin waves and westward propagating Rossby gravity waves are not the primary source to generate the QBO, the GW forcing can seed the oscillation and act as a catalyst to enhance effectiveness of these planetary waves.

Mayr, Hans G.↗

Ocean Tide Loading Computation

September 15,2003 through May 15,2005 This grant funds the maintenance, updating, and distribution of programs for computing ocean tide loading, to enable the corrections for such loading to be more widely applied in space- geodetic and gravity measurements. These programs, developed under funding from the CDP and DOSE programs, incorporate the most recent global tidal models developed from Topex/Poscidon data, and also local tide models for regions around North America; the design of the algorithm and software makes it straightforward to combine local and global models.

Agnew, Duncan Carr↗

15-minute Parker River gap-filled tide height and salinity data, PIE LTER, Plum Island Sound, MA (2014–2023), for ELM PFLOTRAN modeling

This dataset contains 15-minute tide height and salinity data from the Typha site along the Parker River, part of the Plum Island Ecosystems Long Term Ecological Research (PIE LTER) site in Plum Island Sound, Massachusetts (MA) 2014-2023. Tide height (in NAVD88) was compiled from measurements conducted at the mouth of Plum Island Sound and corrected for time lags. Gap-filling of missing periods were done by fitting tidal constituents to the time series. Salinity was measured (and is stored on ESS DIVE ) in 2022 and 2023 using HOBO U24-002 conductivity loggers. River discharge is the most important control on tidal river water salinity at the location (Vallino & Hopkinson, 1998). An artificial neural network was trained to predict river water salinity at the location using Parker River discharge (USGS station 01101000, Parker River at Byfield, MA) and gap-filled salinity observations from a long-term monitoring station ca. 3km downstream from the Typha site (LTER station ‘Middle Road’) as input variables to create continuous time series information. The data set was used in the spin up and simulations of a land surface model coupled to a biogeochemical reaction network (ELM PFLOTRAN) assessing impacts of hydrology and salinity input on methane fluxes in 2022 and 2023 (Sulman et al., 2024). Metadata files ELMPFLOTRAN_tide_salinity_dd.csv and ELMPFLOTRAN_tide_salinity_flmd.csv provide details on site location, data variables, and QA/QC methods .

54 ENVIRONMENTAL SCIENCES↗

Tide Corrections for Coastal Altimetry: Status and Prospects

Knowledge of global oceanic tides has markedly advanced over the last two decades, in no small part because of the near-global measurements provided by satellite altimeters, and especially the long and precise Topex/Poseidon time series e.g. [2]. Satellite altimetry in turn places very severe demands on the accuracy of tidal models. The reason is clear: tides are by far the largest contributor to the variance of sea-surface elevation, so any study of non-tidal ocean signals requires removal of this dominant tidal component. Efforts toward improving models for altimetric tide corrections have understandably focused on deep-water, open-ocean regions. These efforts have produced models thought to be generally accurate to about 2 cm rms. Corresponding tide predictions in shelf and near-coastal regions, however, are far less accurate. This paper discusses the status of our current abilities to provide near-global tidal predictions in shelf and near-coastal waters, highlights some of the difficulties that must be overcome, and attempts to divine a path toward some degree of progress. There are, of course, many groups worldwide who model tides over fairly localized shallow-water regions, and such work is extremely valuable for any altimeter study limited to those regions, but this paper considers the more global models necessary for the general user. There have indeed been efforts to patch local and global models together, but such work is difficult to maintain over many updates and can often encounter problems of proprietary or political nature. Such a path, however, might yet prove the most fruitful, and there are now new plans afoot to try again. As is well known, tides in shallow waters tend to be large, possibly nonlinear, and high wavenumber. The short spatial scales mean that current mapping capabilities with (multiple) nadir-oriented altimeters often yield inadequate coverage. This necessitates added reliance on numerical hydrodynamic models and data assimilation, which in turn necessitates very accurate bathymetry with high spatial resolution. Nonlinearity means that many additional compound tides and overtides must be accounted for in our predictions, which increases the degree of modeling effort and increases the amounts of data required to disentangle closely aliased tides.

Ray, Richard D.↗