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NASA NTRS1994

Geographical representation of radial orbit perturbations due to ocean tides: Implications for satellite altimetry

In analogy to the geographical representation of the zeroth-order radial orbit perturbations due to the static geopotential, similar relationships have been derived for radial orbit perturbations due to the ocean tides. At each location these perturbations are seen to be coherent with the tide height variations. The study of this singularity is of obvious importance to the estimation of ocean tides from satellite altimeter data. We derive analytical expressions for the sensitivity of altimeter derived ocean tide models to the ocean tide force model induced errors in the orbits of the altimeter satellite. In particular, we focus on characterizing and quantifying the nonresonant tidal orbit perturbations, which cannot be adjusted into the empirical accelerations or radial perturbation adjustments commonly used during orbit determination and in altimeter data processing. As an illustration of the utility of this technique, we study the differences between a TOPEX/POSEIDON-derived ocean tide model and the Cartwright and Ray 1991 Geosat model. This analysis shows that nearly 60% of the variance of this difference for M(sub 2) can be explained by the Geosat radial orbit eror due to the omission of coefficients from the GEM-T2 background ocean tide model. For O(sub 1), K(sub 1), S(sub 2), and K(sub 2) the orbital effects account for approximately 10 to 40% of the variances of these differences. The utility of this technique to assessment of the ocean tide induced errors in the TOPEX/POSEIDON-derived tide models is also discussed.

Bettadpur, Srinivas V.↗
NASA NTRS1994

Determination of ocean tides from the first year of TOPEX/POSEIDON altimeter measurements

An improved geocentric global ocean tide model has been determined using 1 year of TOPEX/POSEIDON altimeter measurements to provide corrections to the Cartwright and Ray (1991) model (CR91). The corrections were determined on a 3 deg x 3 deg grid using both the harmonic analysis method and the response method. The two approaches produce similar solutions. The effect on the tide solution of simultaneously adjusting radial orbit correction parameters using altimeter measurements was examined. Four semidiurnal (N(sub 2), M(sub 2), S(sub 2) and K(sub 2)), four diurnal (Q(sdub 1), O(sub 1), P(sub 1), and K(sub 1)), and three long-period (S(sub sa), M(sub m), and M(sub f)) constituents, along with the variations at the annual frequency, were included in the harmomnic analysis solution. The observed annual variations represents the first global measurement describing accurate seasonal changes of the ocean during an El Nino year. The corrections to the M(sub 2) constituent have an root mean square (RMS) of 3.6 cm and display a clear banding pattern with regional highs and lows reaching 8 cm. The improved tide model reduces the weighted altimeter crossover residual from 9.8 cm RMS, when the CR91 tide model is used, to 8.2 cm on RMS. Comparison of the improved model to pelagic tidal constants determined from 80 tide gauges gives RMS differences of 2.7 cm for M(sub 2) and 1.7 cm for K(sub 1). Comparable values when the CR91 model is used are 3.9 cm and 2.0 cm, respectively. Examination of TOPEX/POSEIDON sea level anomaly variations using the new tide model further confirms that the tide model has been improved.

Ma, X. C.↗
NASA NTRS2013

Precise Comparisons of Bottom-Pressure and Altimetric Ocean Tides

A new set of pelagic tide determinations is constructed from seafloor pressure measurements obtained at 151 sites in the deep ocean. To maximize precision of estimated tides, only stations with long time series are used; median time series length is 567 days. Geographical coverage is considerably improved by use of the international tsunami network, but coverage in the Indian Ocean and South Pacific is still weak. As a tool for assessing global ocean tide models, the data set is considerably more reliable than older data sets : the root-mean-square difference with a recent altimetric tide model is approximately 5 mm for the M2 constituent. Precision is sufficiently high to allow secondary effects in altimetric and bottom-pressure tide differences to be studied. The atmospheric tide in bottom pressure is clearly detected at the S1, S2, and T2 frequencies. The altimetric tide model is improved if satellite altimetry is corrected for crustal loading by the atmospheric tide. Models of the solid body tide can also be constrained. The free corenutation effect in the K1 Love number is easily detected, but the overall estimates are not as accurate as a recent determination with very long baseline interferometry.

tides↗
DOE OSTI2025

A cross-dimensional analysis of data-driven short-term load forecasting methods with large-scale smart meter data

Electricity load forecasting is essential to utility operation and power grid stability. A wide spectrum of data-driven methods, ranging from linear regression models to more recent deep learning models have been adopted to forecast electric load over the years. However, there still lacks a holistic evaluation of the applicability of conventional statistical and machine learning based algorithms with respect to different temporal and spatial scopes, computational requirements, and sensitivity of model-tuning. Enabled by a large-scale electricity load profile dataset of over 40,000 residential customers in a utility region, we conducted a cross-dimensional analysis of data-driven load forecasting methods. Three regression-based and seven deep learning algorithms with different model configurations were evaluated in terms of their overall and peak load prediction accuracy, and training burdens, across spatial aggregation levels ranging from the transformer, feeder, substation, to neighborhood. We found, first, the load forecasting accuracy is constrained by a predictability boundary, influenced by the forecasting horizon and spatial aggregation level. Specifically, RandomForest, XGBoost, TFT, TSMixer, and TiDE models achieved less than 10 % prediction error for up to 96-h ahead forecasting for district, substation, and feeder levels, while other models struggle at long-horizon predictions; Second, for winter and summer peak load dates, most models were able to predict the peak demand timing within ± 1 h, but the prediction percentage error varied by models, with TFT and TiDE models being the top performers; Third, models with similar prediction accuracy can differ in training burden by an order of magnitude. Therefore, choosing model configurations that balance prediction performance and computational resource is an important practical consideration for large-scale deployment of the machine learning based load forecasting. The outcome of this study can guide researchers and practitioners to choose the proper load forecasting algorithms based on their problem scope, required accuracy, and available resources. The predictability boundary can serve as a benchmark for electricity load forecasting problems with new algorithms and datasets.

Li, Han↗
NASA NTRS2011

Observing and Modeling Long-Period Tidal Variations in Polar Motion

By exchanging angular momentum with the solid Earth, ocean tides cause the Earth's rotation to change. While hydrodynamic tide models have been used to study the effect of ocean tides on polar motion, it is shown here that none of the published models can fully account for the observed variations. An empirical ocean tide model is therefore determined by fitting periodic terms at the tidal frequencies to polar motion excitation observations, from which atmospheric and non-tidal oceanic effects were removed. While the empirical ocean tide model does fully account for allof the observed tidal power, tests indicate that the model may not have completely converged. So better models of the effects of ocean tides on polar motion are still needed, both dynamical and empirical.

tides↗
NASA NTRS1990

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Dickman, S. R.↗
NASA NTRS1994

Accuracy assessment of the large-scale dynamic ocean topography from TOPEX/POSEIDON altimetry

The quality of TOPEX/POSEIDON determinations of the global scale dynamic ocean topography have been assessed by determining mean topography solutions for successive 10-day repeat cycles and by examining the temporal changes in the sea surface topography to identify known features. The assessment is based on the analysis of TOPEX altimeter data cycles 1 through 36. Important errors in the tide model used to correct the altimeter data have been identified. The errors were reduced significantly by use of a new tide model derived with the TOPEX/POSEIDON measurements. Maps of the global 1-year mean topography, produced using four of the most accurate of the marine geoid, show that the largest error in the dynamic ocean topography show expected features, such as the known annual hemispherical sea surface rise and fall and the seasonal variability due to monsoon influence in the Indian Ocean. Changes in the sequence of 10-day topography maps show the development and propagation of an equatorial Kelvin wave in the Pacific beginning in December 1992 with a propagation velocity of approximately 3 m/s. The observations are consistent with observed changes in the equatorial trade winds, and with tide gauge and other in situ observations of the strengthening of the El Nino. Comparison of TOPEX-determine sea surface height at points near oceanic tide gauges shows agreement at the 4 cm root-mean-square (RMS) level over the tropical Pacific. The results show that the TOPEX altimeter data set can be used to map the ocean surface with a temporal resolution of 10 days and an accuracy which is insonsistent with traditional in situ methods for the determination of sea level variations.

Tapley, B. D.↗
NASA NTRS1999

Improvement of TOPEX/POSEIDON and Jason-1 Geophysical Data Record for Global Change Studies and Coastal Applications

The Earth's modem climate change has been characterized by interlinked changes in temperature, CO2, ice sheets and sea level. Global sea level change is a critical indicator for study of contemporary climate change. Sea level rise appears to have accelerated since the ice sheet retreats have stopped some 5000 years ago and it is estimated that the sea level rise has been approx. 15 cm over the last century. Contemporary radar altimeters represent the only technique capable of monitoring global sea level change with accuracy approaching 1 mm/yr and with a temporal scale of days and a spatial scale of 100 km or longer. This report highlights the major accomplishments of the TOPEX/POSEIDON (T/P) Extended Mission and Jason-1 science investigation. The primary objectives of the investigation include the calibration and improvement of T/P and Jason-1 altimeter data for global sea level change and coastal tide and circulation studies. The scientific objectives of the investigation include: (1) the calibration and improvement of T/P and Jason-1 data as a reference measurement system for the accurate cross-linking with other altimeter systems (Seasat, Geosat, ERS-1, ERS-2, GFO-1, and Envisat), (2) the improved determination and the associated uncertainties of the long-term (15-year) global mean sea level change using multiple altimeters, (3) the characterization of the sea level change by analyses of independent data, including tide gauges, sea surface temperature, and (4) the improvement coastal radar altimetry for studies including coastal ocean tide modeling and coastal circulation. Major accomplishments of the investigation include the development of techniques for low-cost radar altimeter absolute calibration (including the associated GPS-buoy technology), coastal ocean tide modeling, and the linking of multiple altimeter systems and the resulting determination of the 15-year (1985-1999) global mean sea level variations. The current rate of 15-year sea level rise observed by multiple satellite altimetry is +2.3 +/- 1.2 mm/yr, which is in general agreement with the analysis of sparsely distributed tide gauge measurements for the same data span, and represents the first such determination of sea level change in its kind.

Shum, C. K.↗
NASA NTRS1995

Revised predictions of long-period ocean tidal effects on Earth's rotation rate

The rotational response of Earth to long-period tidal forces, embodied in a 'zonal response function,' can be expected to vary with frequency because of variable contributions by the oceans, mantle, and core. The zonal response function has been estimated from 9 years of International Radio Interferometric Surveying (IRIS) universal time (UT1) data and compared with theoretical predictions, using a spherical harmonic tide model to compute the oceans' dynamic response, at semiannual, monthly, fortnightly, and 9-day lunisolar tidal frequencies. Different amounts of mantle anelasticity have been considered for both the oceanic and soild earth responses; predictions have been made assuming axial core-mantle coupling which is either complete or absent. Additionally, an extensive recalibration of the ocean model's frictional parameters was performed using constraints derived in part from Space92 polar motion data; zonal response function predictions have also been made employing this recalibrated ocean tide model. Our results indicate that any amount of core coupling can be ruled out at a fortnightly period and probably at a 9-day period, but not at a monthly period. Our results also suggest that the mantle responds purely elastically at a 9-day period but may behave increasingly anelastically at longer periods. A simple dispersive rule is postulated for periods ranging up to the 14-month Chandler wobble period.

Dickman, S. R.↗
NASA NTRS1994

Diurnal and semidiurnal variations in Earth orientation determined from LAGEOS laser ranging

Variations in universal time and polar motion due to ocean tides at nearly diurnal and nearly semidiurnal frequencies are determined from analysis of laser ranging to the LAGEOS satellite over the period from 1987 to 1992. The adjusted diurnal tides were K(sub 1), S(sub 1), P(sub 1), O(sub 1), and Q(sub 1), while the semidiurnal tides were K(sub 2), S(sub 2), M(sub 2), and N(sub 2). A formulation was used that explicitly separated prograde and retrograde terms in the polar motion in order to eliminate aliasing from the singularity of retrograde wobble with long period orbit error and nutation. The results are compared to other experimentally derived observations from very long baseline interferometry (VLBI) and with predictions from an ocean tide model. The results of this study were well with those from the VLBI studies, typically at the 2-3 microsecond level in universal time and 30-50 microarc sec (muas) level in polar motion. The agreement with predictions from the ocean tide model were roughly a factor of 3 worse for UT although better for polar motion, particularly in the diurnal band.

Watkins, Michael M.↗
DOE OSTI2022

Application-specific optimal model weighting of global climate models: A red tide example

Global climate models (GCMs) and Earth system models (ESMs) provide many climate services with environmental relevance. The High Resolution Model Inter-comparison Project (HighResMIP) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) provides model runs of GCMs and ESMs to address regional phenomena. Developing a parsimonious ensemble of CMIP6 requires multiple ensemble methods such as independent-model subset selection, prescreening-based subset selection, and model weighting. The work presented here focuses on application-specific optimal model weighting, with prescreening-based subset selection. As such, independent ensemble members are categorized, selected, and weighted based on their ability to reproduce physically-interpretable features of interest that are problem-specific. We discuss the strengths and caveats of optimal model weighting using a case study of red tide prediction in the Gulf of Mexico along the West Florida Shelf. Red tide is a common name of specific harmful algal blooms that occur worldwide, causing adverse socioeconomic and environmental impacts. Our results indicate the importance of prescreening-based subset selection as optimal model weighting can underplay robust ensemble members by optimizing error cancellation. Prescreening-based subset selection also provides insights about the validity of the model weights. By illustrating the caveats of using non-representative models when optimal model weighting is used, the findings and discussion of this study are pertinent to many other climate services.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2007

Long Term Mean Local Time of the Ascending Node Prediction

Significant error has been observed in the long term prediction of the Mean Local Time of the Ascending Node on the Aqua spacecraft. This error of approximately 90 seconds over a two year prediction is a complication in planning and timing of maneuvers for all members of the Earth Observing System Afternoon Constellation, which use Aqua's MLTAN as the reference for their inclination maneuvers. It was determined that the source of the prediction error was the lack of a solid Earth tide model in the operational force models. The Love Model of the solid Earth tide potential was used to derive analytic corrections to the inclination and right ascension of the ascending node of Aqua's Sun-synchronous orbit. Additionally, it was determined that the resonance between the Sun and orbit plane of the Sun-synchronous orbit is the primary driver of this error. The analytic corrections have been added to the operational force models for the Aqua spacecraft reducing the two-year 90-second error to less than 7 seconds.

McKinley, David P.↗
NASA NTRS1987

The applicability of satellite altimetry data to tidal models

The characteristics of satellite altimetry data are reviewed, and techniques for incorporating them into numerical tide models are discussed. The relationship between the geocentric tides observed by satellites and the ocean tides measured by gages or predicted by models is explored, and particular attention is given to the differences between deep-water, shelf, and estuarine tidal regimes. It is concluded that a separate tidal solution should always be performed before assimilating satellite data, including calculation of the tides along a single repeated ground track in the case of shelf and estuarine regions. The potential value of the altimetry to be provided by Topex/Poseidon (scheduled launch in 1991) is indicated.

Parke, Michael E.↗
NASA NTRS1993

Dynamic ocean-tide effects on Earth's rotation

This article develops 'broad-band' Liouville equations which are capable of determining the effects on the rotation of the Earth of a periodic excitation even at frequencies as high as semi-diurnal; these equations are then used to predict the rotational effects of altimetric, numerical and 32-constituent spherical harmonic ocean-tide models. The rotational model includes a frequency-dependent decoupled core, the effects of which are especially marked near retrograde diurnal frequencies; and a fully dynamic oceanic response, whose effects appear to be minor despite significant frequency dependence. The model also includes solid-earth effects which are frequency dependent as the result of both anelasticity at long periods and the fluid-core resonance at nearly diurnal periods. The effects of both tidal inertia and relative angular momentum on Earth rotation (polar motion, length of day, 'nutation' and Universal Time) are presented for 32 long- and short-period ocean tides determined as solutions to the author's spherical harmonic tide theory. The lengthening of the Chandler wobble period by the pole tide is also re-computed using the author's full theory. Additionally, using the spherical harmonic theory, tidal currents and their effects on rotation are determined for available numerical and altimetric tide height models. For all models, we find that the effects of tidal currents are at least as important as those of tide height for diurnal and semi-diurnal constituents.

Dickman, S. R.↗
NASA NTRS1995

Seasonal Variations of the Earth's Gravitational Field: An Analysis of Atmospheric Pressure, Ocean Tidal, and Surface Water Excitation

Seasonal variations in the Earth's gravitational field are investigated through the analysis of LAGEOS I satellite laser ranging measurements spanning 1984 to 1992. Global surface pressure data are analyzed; a self-consistent equilibrium ocean tide model is used to compute the effect of the gravitational field on tides. Laser ranging measurements are used to model gravitational field effects.

Laser↗
NASA NTRS2019

The Semiannual and 4.4-Year Modulations of Extreme High Tides

In most places extreme high tides undergo a clear seasonal variation. It is well known that semidiurnal tides tend to peak during equinox seasons, and diurnals during solstice seasons. This is a consequence of the solar and lunar declinations, which when large maximize diurnal tides at the expense of semidiurnals. The semiannual range modulation of tidal extremes for a pure semidiurnal tide is determined mainly by the amplitude of the K2 constituent; a pure diurnal is determined mainly by P1. Mixed tidal regimes tend to experience maxima very roughly around the times of solstice, but not always, with the semiannual modulation generally a complicated function of constituent amplitudes and phases. These modulations are here mapped worldwide by analyzing tidal extremes predicted with a global tide model. The known 4.4-year modulation in extreme tides is a consequence of declinational and perigean effects coming in and out of phase. The phase of the 4.4-year modulation is controlled by the phase of the semiannual modulation, irrespective of whether the tide is diurnal, semidiurnal, or mixed.

Ray, R. D.↗
NASA NTRS1995

Minutes of TOPEX/POSEIDON Science Working Team Meeting and Ocean Tides Workshop

This third TOPEX/POSEIDON Science Working Team meeting was held on December 4, 1994 to review progress in defining ocean tide models, precision Earth orbits, and various science algorithms. A related workshop on ocean tides convened to select the best models to be used by scientists in the Geophysical Data Records.

Fu, Lee-Lueng↗