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The spectra of polar motion excitation functions exhibit enhanced power in the fortnightly tidal band. This enhanced power is attributed to ocean tidal excitation. Ocean tide models predict polar motion excitation effects that differ with each other, and with observations, by factors as large as 2-3. There is a need for inproved models for the effect of long-period ocean tides on Earth's rotation.
The NASA GSFC DORIS analysis center has provided weekly DORIS solutions from November 1992 to January 2009 (839 SINEX files) of station positions and Earth Orientation Parameters for inclusion in the DORIS contribution to ITRF2008. The NASA GSFC GEODYN orbit determination software was used to process the orbits and produce the normal equations. The weekly SINEX gscwd 10 submissions included DORIS data from Envisat, TOPEX!Poseidon, SPOT-2, SPOT-3, SPOT-4, SPOT-5. The orbits were mostly seven days in length (except for weeks with data gaps or maneuvers). The processing used the GRACE-derived EIGEN-GL04S1 gravity model, updated modeling for time-variable gravity, the GOT4.7 ocean tide model and tuned satellite-specific macromodels for SPOT -2, SPOT -3, SPOT -4, SPOT-5 and TOPEX/Poseidon. The University College London (UCL) radiation pressure model for Envisat improves nonconservative force modeling for this satellite, reducing the median residual empirical daily along-track accelerations from 3.75 x 10-9 m/s(exp 2) with the a priori macromodel to 0.99 x 10-9 m/s2 with the UCL model. For the SPOT and Envisat DORIS satellite orbits from 2003 to 2008, we obtain average RMS overlaps of 0.8-0.9 cm in the radial direction, 2.1-3.4 cm cross-track, and 1.7-2.3 cm along-track. The RMS orbit differences between Envisat DORIS-only and SLR & DORIS orbits are 1.1 cm radially, 6.4 cm along-track and 3.7 cm cross-track and are characterized by systematic along-track mean offsets due to the Envisat DORIS system time bias of +/- 5-1O micro s. We obtain a good agreement between the geometrically-determined geocenter parameters and geocenter parameters determined dynamically from analysis of the degree one terms of the geopotential. The intrinsic RMS weekly position repeatability with respect to the IDS-3 combination ranges from 2.5 to 3.0 cm in 1993-1994 to 1.5 cm in 2007-2008.
The aim of this paper is to give an assessment to TOPEX/POSEIDON data users of the two available oceanic tidal corrections, which are based on the Schwiderski model (SCH) and the Cartwright and Ray model (CR), respectively. Large instantaneous differences are observed between the two corrections, and use of either model may sometimes lead to inadequate understanding of the remaining oceanic signals. In this paper we give an objective comparison of SCH and CR models and point out the major features of both models. Our methodology is applicable to the validating and testing of future tide models that will soon be appearing.
It is commonplace to begin talks on this topic by noting that oceanographic data are too scarce and sparse to provide complete initial and boundary conditions for large-scale ocean models. Even considering the availability of remotely-sensed data such as radar altimetry from the TOPEX and ERS-1 satellites, a glance at a map of available subsurface data should convince most observers that this is still the case. Data are still too sparse for comprehensive treatment of interannual to interdecadal climate change through the use of models, since the new data sets have not been around for very long. In view of the dearth of data, we must note that the overall picture is changing rapidly. Recently, there have been a number of large scale ocean analysis and prediction efforts, some of which now run on an operational or at least quasi-operational basis, most notably the model based analyses of the tropical oceans. These programs are modeled on numerical weather prediction. Aside from the success of the global tide models, assimilation of data in the tropics, in support of prediction and analysis of seasonal to interannual climate change, is probably the area of large scale ocean modeling and data assimilation in which the most progress has been made. Climate change is a problem which is particularly suited to advanced data assimilation methods. Linear models are useful, and the linear theory can be exploited. For the most part, the data are sufficiently sparse that implementation of advanced methods is worthwhile. As an example of a large scale data assimilation experiment with a recent extensive data set, we present results of a tropical ocean experiment in which the Kalman filter was used to assimilate three years of altimetric data from Geosat into a coarsely resolved linearized long wave shallow water model. Since nonlinear processes dominate the local dynamic signal outside the tropics, subsurface dynamical quantities cannot be reliably inferred from surface height anomalies. Because of its potential for large scale synoptic coverage of the deep ocean, acoustic travel time data should be a natural complement to satellite altimetry. Satellite data give us vertical integrals associated with thermodynamic and dynamic processes.
We will analyze the TOPEX/POSEIDON data using techniques developed for Geosat, although the more accurate TOPEX/POSEIDON data will enable a wider range of problems to be addressed. Our proposed investigations will have five distinct areas: (1) a description of global sea level variability; (2) tropical ocean dynamics; (3) coupled models for El Nino prediction; (4) structure of the lithosphere; and (5) global tide model improvement.
A numerical ocean tide model has been developed and tested using highly accurate TOPEX/Poseidon (T/P) tidal solutions. The hydrodynamic model is based on time stepping a finite difference approximation to the non-linear shallow water equations. Two novel features of our implementation are a rigorous treatment of self attraction and loading (SAL), and a physically based parameterization for internal tide (IT) radiation drag. The model was run for a range of grid resolutions, and with variations in model parameters and bathymetry. For a rational treatment of SAL and IT drag, the model run at high resolution (1/12 degree) fits the T/P solutions to within 5 cm RMS in the open ocean. Both the rigorous SAL treatment and the IT drag parameterization are required to obtain solutions of this quality. The sensitivity of the solution to perturbations in bathymetry suggest that the fit to T/P is probably now limited by errors in this critical input. Since the model is not constrained by any data, we can test the effect of dropping sea-level to match estimated bathymetry from the last glacial maximum (LGM). Our results suggest that the 100 m drop in sea-level in the LGM would have significantly increased tidal amplitudes in the North Atlantic, and increased overall tidal dissipation by about 40%. However, details in tidal solutions for the past 20 ka are sensitive to the assumed stratification. IT drag accounts for a significant fraction of dissipation, especially in the LGM when large areas of present day shallow sea were exposed, and this parameter is poorly constrained at present.
A procedure for obtaining a parameterization of the marine geoid for suitable orthogonality properties in altimetry data is discussed. The application of the technique to the Puerto Rico trench is explained and a map of the data is developed. The Goddard Earth Model (GEM-6) is described to show the method for determining the earth gravity field using data obtained from satellite tracking stations. The derivation of a global ocean tide model from satellite data is explained. The influence of solid earth and ocean tides on the inclination of GEOS-1 is plotted. The delineation of the geographical fracture pattern and boundary system of the tectonic plates using ERTS satellite is shown.
Abstract This study investigates changes and uncertainties to cool‐season (November‐March) storm tides along the U.S. northeast coast in the 21st century under the high RCP8.5 emission scenario compared to late 20th century. A high‐fidelity (50‐m coastal resolution) hydrodynamic storm tide model is forced with three dynamically downscaled regional climate models (RCMs) over three decadal periods (historical, mid‐21st century, and late‐21st century) to project future changes in peak storm tide elevations at coastal counties in the region. While there is no absolute consensus on future changes to storm tides, for any one future decade two out of the three RCMs project an increase at counties along the Hudson River, Delaware River, and northern Chesapeake Bay due to more intense cyclones that track inland of these locations leading to favorable surge generating conditions. The same RCMs also project a decrease at counties facing the open ocean in the mid‐Atlantic Bight as cyclone densities just offshore of the coastline decrease, particularly by late‐century. The greater tidal range in northern areas of the region leads to uncertainty in the magnitude and sign of the projected changes to storm tide levels due to the arbitrary timing of the local tidal stage and the surge‐producing weather event. This random tide‐weather timing is less important in the Chesapeake Bay and unimportant in Albemarle Sound and Pamlico Sound. Similar to other recent studies, we highlight that sea level rise is likely to be more critical than storm climatology for future changes to the cool‐season coastal flooding potential.
As a generalization of the zonal response coefficient first introduced by Agnew and Farrell (1978), the zonal response function kappa of the solid earth-ocean system is defined as the ratio, in the frequency domain, of the tidal change in earth's rotation rate to the tide-generating potential. Amplitudes and phases of kappa for the monthly, fortnightly, and nine-day lunar tides are estimated from 2 1/2 years of VLBI UT1 observations, corrected for atmospheric angular momentum effects using NMC wind and pressure series. Using the dynamic ocean tide model of Dickman (1988, 1989), amplitudes and phases of kappa for an elastic earth-ocean system are predicted. The predictions confirm earlier results which found that dynamic effects of the longer-period ocean tides reduce the amplitude of kappa by about 1 percent.
The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, both analytical and numerical models for the pole tide are constructed. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.
Ocean tidal effects on universal time and polar motion (UTPM) are investigated at four nearly diurnal (K(sub 1), P(sub 1), O(sub 1), and Q(sub 1)) and four nearly semidiurnal (K(sub 2), S(sub 2), M(sub 2), and N(sub 2)) frequencies by analyzing very long baseline interferometry (VLBI) data extending from 1978 to 1992. We discuss limitations of comparisons between experiment and theory for the retograde nearly diurnal polar motion components due to their degeneracy with prograde components of the nutation model. Estimating amplitudes of contributions to the modeled VLBI observables at these eight frequencies produces a statistically highly significant improvement of 7 mm to the residuals of a fit to the observed delays. Use of such an improved UTPM model also reduces the 14-30 mm scatter of baseline lengths about a time-linear model of tectonic motion by 3-14 mm, also withhigh significance levels. A total of 28 UTPM ocean tidal amplitudes can be unambiguously estimated from the data, with resulting UTI and PM magnitudes as large as 21 micro secs and 270 microarc seconds and formal uncertainties of the order of 0.3 micro secs and 5 microarc secs for UTI and PM, respectively. Empirically determined UTPM amplitudes and phases are com1pared to values calculated theoretically by Gross from Seiler's global ocean tide model. The discrepancy between theory and experiment is larger by a factor of 3 for UTI amplitudes (9 micro secs) than for prograde PM amplitudes (42 microarc secs). The 14-year VLBI data span strongly attenuates the influence of mismodeled effects on estimated UTPM amplitudes and phases that are not coherent with the eight frequencies of interest. Magnitudes of coherent and quasi-coherent systematic errors are quantified by means of internal consistency tests. We conclude that coherent systematic effects are many times larger than the formal uncertainties and can be as large as 4 micro secs for UTI and 60 microarc secs for polar motion. On the basis of such ealistic error estimates, 22 of the 31 fitted UTPM ocean tidal amplitudes differ from zero by more than 2 sigma.
TOPEX sea surface height data from the first 300 days of the mission are compared to sea level data from 71 tide gauges. The initial comparison uses sea surface height data processed according to standard procedures as defined in the users handbook. It is found that the median correlations for island and for coastal tide gauges are 0.53 and 0.42, respectively. The analogous root mean square (RMS) differences between the two data sets are 7.9 and 10.4 cm. The comparisons improve significantly when a 60-day harmonic is fit to the differences and removed. This period captures aliased M(sub 2) and S(sub 2) tidal energy that is not removed by the tide model. Making this correction and smoothing the sea surface height data over 25-km along-track segments results in median correlations of 0.58 and 0.46 for the islands and coastal stations, and median RMS differences of 5.8 and 7.7 cm, respectively. Removing once per revolution signals from the sea surface heights results in degraded comparisons with the sea levels. It is also found that a number of stations have poor comparisons due to propagating signals that introduce temporal lags between the altimeter and tide gauge time series. A final comparison is made by eliminating stations where this propagation effect is large, discarding two stations that are suspected to have problems with the sea level data, smoothing over 10-day intervals, and restricting attention to islands gauges. This results in a set of 552 data pairs that have a correlation of 0.66 and a RMS difference of 4.3 cm. The conclusion is that on timescales longer than about 10 days the RMS sea surface height errors are less than or of the order of several centimeters.
We have analyzed 50 ten-day cycles of TOPEX/POSEIDON (T/P) altimeter data to evaluate the ocean dynamic topography and its temporal variations. We have employed data from both the U.S. and French altimeters along with the NASA precision orbits in this analysis. Errors in the diurnal and semidiurnal components of the Cartwright-Ray tide model have been significantly reduced using a correction developed from a combination of JGM-2 and OSU91A was employed, as well as a geoid model based solely on OSU91A. The long wavelengths of the comparisons to historical data, although geoid error still corrupts the dynamic topography for wavelengths shorter than 2500 km. The root mean square (RMS) variability is similar to previous results from Geosat, with bakground 'noise' approaching 3 cm RMS. The computed annual and semiannual variations are also similar to previous Geosat results, although the hemispheric distribution of the annual heating cycle is much better presented in the T/P results. They also compare reasonably well with the Levitus hydrographic compilation in the northern hemisphere, although the T/P variations generally have larger amplitudes. Ten-day average maps of variations in sea level compare well with simulations measurements at ocean tide gauges, with RMS differences of less than 4 cm and correlations greater than 0.6 for most of the island gauges. Time-longitude plots of these sea level variations at different latitudes in the Pacific clearly show the presence of equatorial Kelvin waves and Rossby waves, with the wave speeds agreeing well with theoretical and observed values. Measurement of variations in global sea level over cycles 2-51 have an RMS variability of 6.3 mm and a rate of change of -3.5 +/- 8 mm/yr, the uncertainty primarily due to insufficient averaging of the interannual and periodic sea level variations. These results show that the accuracy of the T/P measurements of sea level has dramatically improved over previous missions, with estimated time variable errors of 4 cm or less. Although geographically correlated orbit errors have also been reduced to the few centimeter level, further improvement in determinations of the mean dynamic topography will be difficult to obtain until a more accurate model of the marine geoid is available.
Abstract This study proposes and assesses a methodology to obtain high-quality probabilistic predictions and uncertainty information of near-landfall tropical cyclone–driven (TC-driven) storm tide and inundation with limited time and resources. Forecasts of TC track, intensity, and size are perturbed according to quasi-random Korobov sequences of historical forecast errors with assumed Gaussian and uniform statistical distributions. These perturbations are run in an ensemble of hydrodynamic storm tide model simulations. The resulting set of maximum water surface elevations are dimensionality reduced using Karhunen–Loève expansions and then used as a training set to develop a polynomial chaos (PC) surrogate model from which global sensitivities and probabilistic predictions can be extracted. The maximum water surface elevation is extrapolated over dry points incorporating energy head loss with distance to properly train the surrogate for predicting inundation. We find that the surrogate constructed with third-order PCs using elastic net penalized regression with leave-one-out cross validation provides the most robust fit across training and test sets. Probabilistic predictions of maximum water surface elevation and inundation area by the surrogate model at 48-h lead time for three past U.S. landfalling hurricanes (Irma in 2017, Florence in 2018, and Laura in 2020) are found to be reliable when compared to best track hindcast simulation results, even when trained with as few as 19 samples. The maximum water surface elevation is most sensitive to perpendicular track-offset errors for all three storms. Laura is also highly sensitive to storm size and has the least reliable prediction. Significance Statement The purpose of this study is to develop and evaluate a methodology that can be used to provide high-quality probabilistic predictions of hurricane-induced storm tide and inundation with limited time and resources. This is important for emergency management purposes during or after the landfall of hurricanes. Our results show that sampling forecast errors using quasi-random sequences combined with machine learning techniques that fit polynomial functions to the data are well suited to this task. The polynomial functions also have the benefit of producing exact sensitivity indices of storm tide and inundation to the forecasted hurricane properties such as path, intensity, and size, which can be used for uncertainty estimation. The code implementing the presented methodology is publicly available on GitHub.
Over the years, hurricane track and intensity forecasts and storm surge models and the digital terrain and bathymetry data they depend on have improved significantly. Strides have also been made in knowledge of the detailed variation of the surface wind field driving the surge. The area of least improvement has been in obtaining data on the details of the temporal/spatial variation of the storm surge dome of water as it evolves and inundates the land to evaluate the performance of the numerical models. Tide gages in the vicinity of the landfall are frequently destroyed by the surge. Survey crews dispatched after the event provide no temporal information and only indirect indications of the maximum surge envelope over land. The landfall of Hurricane Bonnie on 26 August 1998, with a surge less than 2 m, provided an excellent opportunity to demonstrate the potential benefits of direct airborne measurement of the temporal/spatial evolution of storm surge. Despite a 160 m variation in aircraft altitude, an 11.5 m variation in the elevation of the mean sea surface relative to the ellipsoid over the flight track, and the tidal variation over the 5 hour data acquisition interval, a survey-quality Global Positioning System (GPS) aircraft trajectory allowed the NASA Scanning Radar Altimeter carried by a NOAA hurricane research aircraft to produce storm surge measurements that generally fell between the predictions of the NOAA SLOSH model and the North Carolina State University storm surge model.
In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.
This year, my team made a very productive use of LANL IC time. Four papers were published that used IC resources, and two more are under review. These publications fall into three categories: 1.) Improving tide modeling in the global ocean by adding self attraction and loading (Barton et. al. 2022), ice shelf cavities (Pal et al. 2023), and local time stepping (Lilly et al. 2023). 2.) A new sea ice numerical formulation (Capodaglio 2023). 3.) Performance comparisons, methods, and test cases for ocean model development, This includes a verification suite for ocean models (Bishnu, submitted) and a comparison between Julia and Fortran (Strauss, submitted). A new time-stepping method was introduced in Calandrini et al. (2022). These publications, and the use of LANL IC resources, go hand-in-hand with our mentoring efforts to train young scientists. Two of the lead authors are graduate students who are conducting their PhD research: Kristin Barton at the University of Michigan and Jeremy Lilly at Oregon State. These are both their first publications, and they both have DOE funding and DOE mentors. In addition, Bishnu is a post-doctoral researcher at LANL; Strauss conducted his research as a senior in high school; and Capodaglio, Calandrini and Pal are all early-career scientists who were converted to staff in 2021 or 2022. Here we highlight two publications on improvements in tidal modeling: Barton et al. 2022 and Lilly et al. 2023.
The time evolving strain field contains a wealth of information that can be used to interpret subsurface behavior. For example, injecting or removing fluids from reservoirs or aquifers causes deformation that can be used as a diagnostic signal in some cases, while it can interfere with geodetic interpretations in other cases. We've previously demonstrated the feasibility of measuring the strain tensor at a depth of 30m caused by injection into a reservoir at 530m. The observed strain signals were interpreted using four independent analytic and numerical methods that resulted in estimates of the poroelastic properties and geometry of the reservoir that was consistent with data from well logs. However, studies like these are only possible if these deformations can be reliably measured. Years of lab and field work has culminated in the development of a novel borehole strainmeter capable of resolving multiple components of strain using embedded optical fibers configured as Michelson interferometers. It features four horizontal gauges separated by 45° to resolve the horizontal strain tensor as well as a vertical strain gauge and a sixth null component for state-of-health monitoring. The downhole sensing package also includes an open pipe through its center for grout circulation during single-trip deployments and a fully welded stainless steel exterior for robustness and longevity. These instruments have a resolution of 2x10-13 strain that can easily measure the solid earth tides. Preliminary data are available from four strainmeters in shale at our Oklahoma site and four in compacted sand and gravel in Utah. These are deployed from 40-60m, except one of the strainmeters in Oklahoma is deployed at 500m. The data include strains from the initial grout curing, comparisons to predicted earth tide models and in-situ calibration results, barometric pressure admittances and spectral analyses as well as signals from underground injections and surface waves from teleseismic events. Preliminary analyses indicate behavior consistent with other strainmeter deployments, and comparison to data from a Gladwin strainmeter at the Oklahoma site validate the performance of the new design. Analyses from a suite of six well tests at the Oklahoma site show for the first time how the strain tensor field varies with location during well testing.