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NASA NTRS1996

Demonstration of a Real Time Capability to Produce Tidal Heights and Currents for Naval Operational Use: A Cast Study for the West Coast of Africa (Liberia)

This report documents an existing capability to produce operationally relevant products on sea level and currents from a tides/storm surge model for any coastal region around the world within 48 hours from the time of the request. The model is ready for transition to the Naval Oceanographic Office (NAVOCEANO) for potential contingency use anywhere around the world. A recent application to naval operations offshore Liberia illustrates this. Mississippi State University, in collaboration with the University of Colorado and NAVOCEANO, successfully deployed the Colorado University Rapidly Relocatable Nestable Tides and Storm Surge (CURReNTSS) model that predicts sea surface height, tidal currents and storm surge, and provided operational products on tidal sea level and currents in the littoral region off south-western coast of Africa. This report summarizes the results of this collaborative effort in an actual contingency use of the relocatable model, summarizes the lessons learned, and provides recommendations for further evaluation and transition of this modeling capability to operational use.

CASE STUDIES↗

NASA NTRS1986

Another look at North Sea pole tide dynamics

The mechanism proposed by Wunsch (1974) to explain pole tide observations in the North Sea is evaluated. Wunsch's equations governing pole tide in the North Sea are presented, and solutions for correcting the depth, stream function, and deviation of the tidal height from the equilibrium values are described. The similarity between the Stokes paradox and the tidal equations of the North Sea, and the need for inclusion of inertial terms in the tidal equations are discussed.

Dickman, S. R.↗

NASA NTRS2021

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↗

NASA NTRS1984

An objective analysis technique for extrapolating tidal fields

An interpolation technique which allows accurate extrapolation of tidal height fields in the ocean basins by making use of selected satellite altimetry measurements and/or conventional gauge measurements was developed and tested. A normal mode solution for the Atlantic and Indian Oceans was obtained by means of a finite difference grid. Normal mode amplitude maps are presented.

Sanchez, B. V.↗

NASA NTRS1985

The relations between the linear and bilinear atmospheric tidal fields in geometric height and in log-pressure coordinates

Theoretical models of planetary-atmosphere tidal fields are examined analytically, comparing models based on geometric-height coordinates with those employing log-pressure coordinates. The relationship between the linearized meteorological variables in the two systems is explored for classical tidal theory and its reduction to the Laplace tidal equation, and it is shown that identical horizontal and vertical equations are obtained. Also considered are the tidal zonal-mean bilinear flux convergences and their Eliassen-Palm formulations. Numerical results for problems involving the earth and Mars atmospheres are presented in graphs and discussed.

Zurek, Richard W.↗

NASA NTRS1994

Aliased tidal errors in TOPEX/POSEIDON sea surface height data

Alias periods and wavelengths for the M(sub 2, S(sub 2), N(sub 2), K(sub 1), O(sub 1), and P(sub 1) tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelenghts calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K(sub 1) constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are likely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M(sub 2) alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M(sub 2), N(sub 2) and O(sub 1) fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S(sub 2), K(sub 1) and P(sub 1) varies smoothly with latitude. S(sub 2) is strongly aliased for latitudes within 50 degress of the equator, while K(sub 1) and P(sub 1) are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented.

Schlax, Michael G.↗

NASA NTRS1977

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Volland, H.↗

NASA NTRS2017

Manuel Johnson's Tide Record at St. Helena

The astronomer Manuel Johnson, a future President of the Royal Astronomical Society, recorded the ocean tides with his own instrument at St. Helena in 1826-1827, while waiting for an observatory to be built. It is an important record in the history of tidal science, as the only previous measurements at St. Helena had been those made by Nevil Maskelyne in 1761, and there were to be no other systematic measurements until the late 20th century. Johnsons tide gauge, of a curious but unique design, recorded efficiently the height of every tidal high and low water for at least 13 months, in spite of requiring frequent re-setting. These heights compare very reasonably with a modern tidal synthesis based on present-day tide gauge measurements from the same site.Johnsons method of timing is unknown, but his calculations of lunar phases suggest that his tidal measurements were recorded in Local Apparent Time. Unfortunately, the recorded times are found to be seriously and variably lagged by many minutes. Johnsons data have never been fully published, but his manuscripts have been safely archived and are available for inspection at Cambridge University. His data have been converted to computerfiles as part of this study for the benefit of future researchers.

Cartwright, David E.↗

NASA NTRS1974

Tidal waves within the thermosphere

The eigenfunctions of the atmosphere (the Hough functions within the lower atmosphere below about 100 km) change their structure and their propagation characteristics within the thermosphere due to dissipation effects such as heat conduction, viscosity, and ion drag. Wave dissipation can be parameterized to a first-order approximation by a complex frequency, the imaginary term of which simulates an effective ion drag force. It is shown how the equivalent depth, the attenuation, and the vertical wavelength of the predominant symmetric diurnal tidal modes change with height as functions of effective ion drag. The boundary conditions of tidal waves are discussed, and asymptotic solutions for the wave parameters like pressure, density, temperature, and wind generated by a heat input proportional to the mean pressure are given. Finally, diffusion effects upon the minor constituents within the thermosphere are described.

Volland, H.↗

NASA NTRS1981

A diurnal resonance in the ocean tide and in the earth's load response due to the resonant free 'core nutation'

The effects of the oceans, which are subject to a resonance due to a free rotational eigenmode of an elliptical, rotating earth with a fluid outer core having an eigenfrequency of (1 + 1/460) cycle/day, on the body tide and nutational response of the earth to the diurnal luni-tidal force are computed. The response of an elastic, rotating, elliptical, oceanless earth with a fluid outer core to a given load distribution on its surface is first considered, and the tidal sea level height for equilibrium and nonequilibrium oceans is examined. Computations of the effects of equilibrium and nonequilibrium oceans on the nutational and deformational responses of the earth are then presented which show small but significant perturbations to the retrograde 18.6-year and prograde six-month nutations, and more important effects on the earth body tide, which is also resonant at the free core notation eigenfrequency.

Wahr, J. M.↗

NASA NTRS1972

The problem of the boundary conditions in thermosphere dynamics.

A simple analytic solution for the generation and propagation of tidal waves at thermospheric heights is presented. It is used to show that a unique solution of tidal wave propagation within the thermosphere depends on the boundary conditions of the model, and that radiation conditions lead to such a unique solution.

Volland, H.↗

NASA NTRS1973

A numerical study of three-dimensional diurnal variations within the thermosphere.

A thermosphere model with a realistic temperature profile is assumed. Heat conduction waves are introduced in addition to gravity waves. The temporal and spatial distribution of ion-neutral collisions is taken into account. However, the influence of viscosity waves is neglected. Viscosity-wave effects are simulated by an effective height-dependent collision number. Numerical calculations are conducted of the generation and propagation of two of the most important symmetric tidal waves at thermospheric heights. The influence of the solar EUV-heat upon the generation of the two tidal modes is investigated.

Volland, H.↗

NASA NTRS1989

Global behavior of the height/seasonal structure of tides between 40 deg and 60 deg latitude

The radars utilized are meteor (2), medium frequency (2) and the new low frequency (1) systems: analysis techniques were exhaustively studied internally and comparatively and are not thought to affect the results. Emphasis is placed upon the new height-time contours of 24-, 12-h tidal amplitudes and phases, which best display height and seasonal structures; where possible high resolution (10 d) is used (Saskatoon), but all stations provide monthly mean resolution. At these latitudes the diurnal tide is generally smaller than the semidiurnal, and displays more variability. However, there is a tendency for vertical wavelengths and amplitudes to be larger during summer months. On occasions in winter and fall, wavelengths may be less than 50 km. The dominant semidiurnal tide shows significant regular season structure; wavelengths are generally small (about 50 km) in winter, large in summer (equal to or greater than 100 km), and these states are separated by rapid equinoctial transitions. There is some evidence for less regularity toward 40 deg. Coupling with mean winds is apparent. Data from earlier ATMAP campaigns are mentioned, and reasons for their inadequacies presented.

Manson, A. H.↗

NASA NTRS1990

Zonal superrotation above Venus' cloud base induced by the semidiurnal tide and the mean meridional circulation

The equilibrium zonal wind structure resulting from the interaction of the semidiurnal tide and the mean meridional circulation driven by the zonally averaged solar heating above the Venus cloud base were calculated. The results show that the tidal mechanism proposed by Fels and Lindzen (1974) can account for a substantial fraction (and possibly all) of the increase of the equatorial wind speed above the cloud base. Above the cloud tops, tidal deceleration may be too small to produce the zonal wind decrease with height inferred from thermal data. Tidal forcing does not explain the superrotation below the clouds, and additional eddy sources are needed to account for the zonal wind structure at mid and high latitudes.

Hou, Arthur Y.↗

NASA NTRS2012

Twenty Years of Progress on Global Ocean Tides: The Impact of Satellite Altimetry

At the dawn of the era of high-precision altimetry, before the launch of TOPEX/Poseidon, ocean tides were properly viewed as a source of noise--tidal variations in ocean height would represent a very substantial fraction of what the altimeter measures, and would have to be accurately predicted and subtracted if altimetry were to achieve its potential for ocean and climate studies. But to the extent that the altimetry could be severely contaminated by tides, it also represented an unprecedented global-scale tidal data set. These new data, together with research stimulated by the need for accurate tidal corrections, led to a renaissance in tidal studies in the oceanographic community. In this paper we review contributions of altimetry to tidal science over the past 20 years, emphasizing recent progress. Mapping of tides has now been extended from the early focus on major constituents in the open ocean to include minor constituents, (e.g., long-period tides; non-linear tides in shelf waters, and in the open ocean), and into shallow and coastal waters. Global and spatially local estimates of tidal energy balance have been refined, and the role of internal tide conversion in dissipating barotropic tidal energy is now well established through modeling, altimetry, and in situ observations. However, energy budgets for internal tides, and the role of tidal dissipation in vertical ocean mixing remain controversial topics. Altimetry may contribute to resolving some of these important questions through improved mapping of low-mode internal tides. This area has advanced significantly in recent years, with several global maps now available, and progress on constraining temporally incoherent components. For the future, new applications of altimetry (e.g., in the coastal ocean, where barotropic tidal models remain inadequate), and new mission concepts (studies of the submesoscale with SWOT, which will require correction for internal tides) may bring us full circle, again pushing further development of tidal models as corrections.

Egbert, Gary↗

NASA NTRS1984

Measurement of the Vertical Gradient of the Semidiurnal Tidal Wind Phase in Winter at the 95 Km Level

When supplemented by absolute reflection height measurements, low frequency wind measurements in the 90-100 km height range become truly competitive in comparison with the more widely used radar meteor wind observations. For example, height profiles of the wind parameters in the so-called meteor zone can be obtained due to the considerable interdiurnal variability of the average nighttime reflection heights controlled by geomagnetic activity. The phase of the semidiurnal tidal wind is particularly height-dependent. The measured vertical gradient of 1/4 h/km in winter corresponds to a vertical wavelength of about 50 km. Wind measurements in the upper atmosphere, at heights between 90 and 100 km, were carried out at the Collm Geophysical Observatory of Karl Marx University Leipzig for a number of years. These measurements use the closely-spaced receiver method and three measuring paths, on 179, 227, and 272 kHz. They take place every day between sunset and sunrise, i.e., nightly. A night in this sense may last as long as 18 hours in winter. Both the measurements and their evaluation are completely automatic, and the prevailing winds and tides are separated.

Schminder, R.↗

NASA NTRS2015

High-Resolution Forest Canopy Height Estimation in an African Blue Carbon Ecosystem

Mangrove forests are one of the most productive and carbon dense ecosystems that are only found at tidally inundated coastal areas. Forest canopy height is an important measure for modeling carbon and biomass dynamics, as well as land cover change. By taking advantage of the flat terrain and dense canopy cover, the present study derived digital surface models (DSMs) using stereophotogrammetric techniques on high-resolution spaceborne imagery (HRSI) for southern Mozambique. A mean-weighted ground surface elevation factor was subtracted from the HRSI DSM to accurately estimate the canopy height in mangrove forests in southern Mozambique. The mean and H100 tree height measured in both the field and with the digital canopy model provided the most accurate results with a vertical error of 1.18-1.84 m, respectively. Distinct patterns were identified in the HRSI canopy height map that could not be discerned from coarse shuttle radar topography mission canopy maps even though the mode and distribution of canopy heights were similar over the same area. Through further investigation, HRSI DSMs have the potential of providing a new type of three-dimensional dataset that could serve as calibration/validation data for other DSMs generated from spaceborne datasets with much larger global coverage. HSRI DSMs could be used in lieu of Lidar acquisitions for canopy height and forest biomass estimation, and be combined with passive optical data to improve land cover classifications.

HRSI↗

NASA NTRS1993

The effect of ocean tides on the earth's rotation as predicted by the results of an ocean tide model

The published ocean tidal angular momentum results of Seiler (1991) are used to predict the effects of the most important semidiurnal, diurnal, and long period ocean tides on the earth's rotation. The separate, as well as combined, effects of ocean tidal currents and sea level height changes on the length-of-day, UT1, and polar motion are computed. The predicted polar motion results reported here account for the presence of the free core nutation and are given in terms of the motion of the celestial ephemeris pole so that they can be compared directly to the results of observations. Outside the retrograde diurnal tidal band, the summed effect of the semidiurnal and diurnal ocean tides studied here predict peak-to-peak polar motion amplitudes as large as 2 mas. Within the retrograde diurnal tidal band, the resonant enhancement caused by the free core nutation leads to predicted polar motion amplitudes as large as 9 mas.

Gross, Richard S.↗