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Physiologically guided approach to characterizing respiratory motion
Purpose: To characterize radiation therapy patient breathing patterns based on measured external surrogate information. Methods: Breathing surrogate data were collected during 4DCT from a cohort of 50 patients including 28 patients with lung cancer and 22 patients without lung cancer. A spirometer and an abdominal pneumatic bellows were used as the surrogates. The relationship between these measurements was assumed to be linear within a small phase difference. The signals were correlated and drift corrected using a previously published method to convert the signal into tidal volume. The airflow was calculated with a first order time derivative of the tidal volume using a window centered on the point of interest and with a window length equal to the CT gantry rotation period. The airflow was compared against the tidal volume to create ellipsoidal patterns that were binned into 25 ml × 25 ml/s bins to determine the relative amount of time spent in each bin. To calculate the variability of the maximum inhalation tidal volume within a free-breathing scan timeframe, a metric based on percentile volume ratios was defined. The free breathing variability metric (κ) was defined as the ratio between extreme inhalation tidal volumes (defined as >93 tidal volume percentile of the measured tidal volume) and normal inhalation tidal volume (defined as >80 tidal volume percentile of the measured tidal volume). Results: There were three observed types of volume-flow curves, labeled Types 1, 2, and 3. Type 1 patients spent a greater duration of time during exhalation withκ = 1.37 ± 0.11. Type 2 patients had equal time duration spent during inhalation and exhalation with κ = 1.28 ± 0.09. The differences between the mean peak exhalation to peak inhalation tidal volume, breathing period, and the 85th tidal volume percentile for Type 1 and Type 2 patients were statistically significant at the 2% significance level. The difference between κ and the 98th tidal volume percentile for Type 1 and Type 2 patients was found to be statistically significant at the 1% significance level. Three patients did not display a breathing stability curve that could be classified as Type 1 or Type 2 due to chaotic breathing patterns. These patients were classified as Type 3 patients. Conclusions: Based on an observed volume-flow curve pattern, the cohort of 50 patients was divided into three categories called Type 1, Type 2, and Type 3. There were statistically significant differences in breathing characteristics between Type 1 and Type 2 patients. The use of volume-flow curves to classify patients has been demonstrated as a physiological characterization metric that has the potential to optimize gating windows in radiation therapy.
ESCAPING PARTICLE FLUXES IN THE ATMOSPHERES OF CLOSE-IN EXOPLANETS. II. REDUCED MASS-LOSS RATES AND ANISOTROPIC WINDS
In Paper I, we presented a one-dimensional hydrodynamic model for the winds of close-in exoplanets. However, close-in exoplanets are tidally locked and irradiated only on the day sides by their host stars. This requires two-dimensional hydrodynamic models with self-consistent radiative transfer calculations. In this paper, for the tidal-locking (two-dimensional radiative transfer) and non-tidal-locking cases (one-dimensional radiative transfer), we constructed a multi-fluid two-dimensional hydrodynamic model with detailed radiative transfer to depict the escape of particles. We found that the tidal forces (the sum of tidal gravity of the star and centrifugal force due to the planetary rotation) supply significant accelerations and result in anisotropic winds. An important effect of the tidal forces is that it severely depresses the outflow of particles near the polar regions where the density and the radial velocity are a factor of a few (ten) smaller than those of the low-latitude regions. As a consequence, most particles escape the surface of the planet from the regions of low latitude. Comparing the tidal-locking and non-tidal-locking cases, we found that their optical depths are very different so that the flows also emerge with a different pattern. In the case of non-tidal locking, the radial velocities at the base of the wind are higher than the meridional velocities. However, in the case of tidal locking, the meridional velocities dominate the flow at the base of the wind, and they can effectively transfer mass and energy from the day sides to the night sides. Further, we also found that the differences of the winds show a middle extent at large radii. This means that the structure of the wind at the base can be changed by the two-dimensional radiative transfer due to large optical depths, but the extent is reduced with an increase in radius. Because the escape is depressed in the polar regions, the mass-loss rate predicted by the non-tidal-locking model, in the order of magnitude of 10{sup 10} g s{sup -1}, is a factor of two lower than that predicted by the one-dimensional hydrodynamic model. The results of tidal locking show that the mass-loss rate is decreased an order of magnitude, only 4.3 Multiplication-Sign 10{sup 9} g s{sup -1}, due to large optical depths on the night side. We also found that the distributions of hydrogen atoms show clear variations from the day side to the night side, thus the origin of the excess absorption in Ly{alpha} should be reexamined using multi-dimensional hydrodynamic models.
Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi
Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.
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.
Disruption of a red giant star by a supermassive black hole and the case of PS1-10jh
The development of a new generation of theoretical models for tidal disruptions is timely, as increasingly diverse events are being captured in surveys of the transient sky. Recently, Gezari et al. reported a discovery of a new class of tidal disruption events: the disruption of a helium-rich stellar core, thought to be a remnant of a red giant (RG) star. Motivated by this discovery and in anticipation of others, we consider tidal interaction of an RG star with a supermassive black hole (SMBH) which leads to the stripping of the stellar envelope and subsequent inspiral of the compact core toward the black hole. Once the stellar envelope is removed the inspiral of the core is driven by tidal heating as well as the emission of gravitational radiation until the core either falls into the SMBH or is tidally disrupted. In the case of the tidal disruption candidate PS1-10jh, we find that there is a set of orbital solutions at high eccentricities in which the tidally stripped hydrogen envelope is accreted by the SMBH before the helium core is disrupted. This places the RG core in a portion of parameter space where strong tidal heating can lift the degeneracy of the compact remnant and disrupt it before it reaches the tidal radius. We consider how this sequence of events explains the puzzling absence of the hydrogen emission lines from the spectrum of PS1-10jh and gives rise to its other observational features.
Mars dust-driven tides and their impact on the thermosphere
It has been known since the early Mariner 6, 7, and 9 missions that dust loading of the lower atmosphere and the subsequent aerosol heating during dusty periods impacts the martian middle and upper atmospheres. A quantitative measure of this lower atmosphere forcing was obtained by the Viking 1 and 2 landers, from which observed amplitudes of semidiurnal surface-pressure oscillations were correlated with normal-incidence dust optical depths. It appears that the dominant semidiurnal mode is a good indicator of global dust content or mean dust optical depth, especially during dust storm events. A classical tidal model that reproduces the surface pressure oscillations measured by these Viking landers in 1977 was used to calculate tidal amplitudes and phases up to approximately 43 km. These tidal characteristics were calculated for various dust optical depth conditions ranging from typical dusty periods to global dust storm times. Reasonable extrapolations can be made to higher altitudes if one assumes that the vertically propagating tidal modes continue to grow without dissipation or breaking. It is very likely that gravity waves also play an important role in the structure and dynamics of the middle atmosphere of Mars, since the large topographical relief should produce vigorous gravity wave fluxes. Semidiurnal tidal modes, significantly enhanced by lower atmosphere dust-induced heating, may indeed propagate to the Mars thermosphere (approximately less than 100 km) before breaking and generating turbulence. The preferential enhancement of the semidiurnal tides during dust storm onset is primarily due to the elevation of the tidal heating source in a very dusty atmosphere. The (2,2) semidiurnal tidal tidal mode was shown to have the largest variation with dust optical depth, as measured by Viking lander instruments. Also, the (2,2) mode has the largest vertical wavelength of all the semidiurnal tidal modes, and thus is most likely to penetrate into the thermosphere before breaking and to modify the largely in situ solar-driven behavior otherwise expected. The tides may also be partially responsible for determining the height of the martian homopause (approximately 125 km).
Evidence for Impact of Galaxy Mergers on Stellar Kinematics of Early-type Galaxies
We provide observational evidence that galaxy mergers significantly affect stellar kinematics of early-type galaxies (ETGs) such as specific stellar angular momentum within the half-light radius (${\lambda }_{{R}_{e}}$) and kinematic misalignment (ψ mis ), using MaNGA integral field unit spectroscopic data that are in the Stripe 82 region of the Sloan Digital Sky Survey. In this study, tidal features around ETGs, which are detected in deep coadded images, are used as direct evidence for mergers that occurred recently. In the case of ETGs that do not have dust lanes, ${\lambda }_{{R}_{e}}$ is lower in ETGs with tidal features than in those without tidal features (median ${\lambda }_{{R}_{e}}$: 0.21 versus 0.39) in all stellar mass and Sérsic index ranges except the most massive bin, so that the fraction of ETGs with tidal features in slow rotators is more than twice as large as that in fast rotators (42% versus 18%). Moreover, ETGs with tidal features have larger ψ mis than those without tidal features (mean ψ mis : 28° versus 15°). By contrast, ETGs with dust lanes are fast rotators, and ETGs with both dust lanes and tidal features have the highest ${\lambda }_{{R}_{e}}$ (median ${\lambda }_{{R}_{e}}$: 0.59) among all ETG categories. In addition, ETGs with dust lanes have small ψ mis regardless of the existence of tidal features (Ψ mis <7$^{°}_{.}$5). Our results can be explained if mergers with different gas fractions generate merger remnants that have different kinematic properties.
Star formation in CALIFA survey perturbed galaxies – II. Star-formation histories and oxygen abundances
ABSTRACT Galaxy evolution is generally affected by tidal interactions. First, in this series, we reported several effects that suggest that tidal interactions contribute to the regulation of star formation (SF). To confirm this, we now compare stellar mass assembly histories and SF look-back time annular profiles between CALIFA survey tidally and non-tidally perturbed galaxies. We pair their respective star-forming regions at the closest stellar mass surface densities to reduce the influence of stellar mass. The assembly histories and annular profiles show statistically significant differences so that higher star-formation rates characterize regions in tidally perturbed galaxies. These regions underwent a more intense (re)activation of SF in the last 1 Gyr. Varying shapes of the annular profiles also reflect fluctuations between suppression and (re)activation of SF. Since gas-phase abundances used to be lower in more actively than in less actively star-forming galaxies, we further explore the plausible presence of metal-poor gas inflows able to dilute such abundances. The resolved relations of oxygen (O) abundance with stellar mass density and with total gas fraction show slightly lower O abundances for regions in tidally perturbed galaxies. The single distributions of O abundances statistically validate this. Moreover, from a metallicity model based on stellar feedback, the mass rate differentials (inflows−outflows) show statistically valid higher values for regions in tidally perturbed galaxies. These differentials, and the metal fractions from the population synthesis, suggest dominant gas inflows in these galaxies. This dominance and the differences in SF through time confirm the previously reported effects of tidal interactions on SF.
A search for stellar structures around nine outer halo globular clusters in the Milky Way
We use deep imaging from the Dark Energy Camera to explore the peripheral regions of nine globular clusters in the outer halo of the Milky Way. Apart from Whiting 1 and NGC 7492, which are projected against the Sagittarius stream, we see no evidence for adjacent stellar populations to indicate any of these clusters is associated with coherent tidal debris from a destroyed host dwarf. We also find no evidence for tidal tails around any of the clusters in our sample; however, both NGC 1904 and 6981 appear to possess outer envelopes. Here, motivated by a slew of recent Gaia -based discoveries, we compile a sample of clusters with robust detections of extra-tidal structure, and search for correlations with orbital properties. While we observe that clusters with tidal tails are typically on moderately or very eccentric orbits that are highly inclined to the Galactic plane and often retrograde, these are neither necessary nor sufficient conditions for the formation of extra-tidal structure. That many objects with tidal tails appear to be accreted leads us to speculate that this lack of consistency may stem from the inhomogeneous dynamical history of the Milky Way globular cluster system. Finally, we note that clusters with prominent stellar envelopes detected in ground-based imaging (such as NGC 1851 and 7089) are now all known from Gaia to possess long tidal tails – experimental confirmation that the presence of an extended envelope is indicative of tidal erosion.
Evidence for Excitation of Polar Motion by Fortnightly Ocean Tides
The second-degree zonal tide raising potential, which is responsible for tidal changes in the Earth's rotation rate and length-of-day, is symmetric about the polar axis and hence can excite the Earth's polar motion only through its action upon nonaxisymmetric features of the Earth such as the oceans. Ocean tidal excitation of polar motion in the diurnal and semidiurnal tidal bands has been previously detected and examined. Here, the detection of ocean tidal excitation of polar motion in the long-period tidal band, specifically at the Mf' (13.63-day) and Mf (13.66-day) tidal frequencies, is reported. Spectra of the SPACE94 polar motion excitation series exhibit peaks at the prograde and retrograde fortnightly tidal periods. After removing effects of atmospheric wind and pressure changes, an empirical model for the effect of the fortnightly ocean tides upon polar motion excitation is obtained by least-squares fitting periodic terms at the Mf and Mf' tidal frequencies to the residual polar motion excitation series. The resulting empirical model is then compared with the predictions of two hydrodynamic ocean tide models.
Constraints on Friction, Dilatancy, Diffusivity, and Effective Stress From Low-Frequency Earthquake Rates on the Deep San Andreas Fault
Families of recurring low-frequency earthquakes (LFEs) within nonvolcanic tremor on the San Andreas Fault in central California are sensitive to tidal stresses. LFEs occur at all levels of the tides, are strongly correlated and in phase with the ~200 Pa shear stresses, and weakly and not systematically correlated with the ~2 kPa tidal normal stresses. Here, we assume that LFEs are small sources that repeatedly fail during shear within a much larger scale, aseismically slipping fault zone and consider two different models of the fault slip: (1) modulation of the fault slip rate by the tidal stresses or (2) episodic slip, triggered by the tides. LFEs are strongly clustered with duration much shorter than the semidiurnal tide; they cannot be significantly modulated on that time scale. The recurrence times of clusters, however, are many times longer than the semidiurnal, leading to an appearance of tidal triggering. In this context we examine the predictions of laboratory-observed triggered frictional (dilatant) fault slip. The undrained end-member model produces no sensitivity to the tidal normal stress, and slip onsets are in phase with the tidal shear stress. The tidal correlation constrains the diffusivity to be less than ~1 × 10 -6 /s and the product of the friction and dilatancy coefficients to be at most 5 × 10 -7 , orders of magnitude smaller than observed at room temperature. In the absence of dilatancy the effective normal stress at failure would be about ~55 kPa. Finally, for this model the observations require intrinsic weakness, low dilatancy, and lithostatic pore fluid.
Warping and tearing of misaligned circumbinary disks around eccentric supermassive black hole binaries
We study the warping and tearing of a geometrically thin, non-self-gravitating disk surrounding binary supermassive black holes on an eccentric orbit. The circumbinary disk is significantly misaligned with the binary orbital plane, and is subject to the time-dependent tidal torques. In principle, such a disk is warped and precesses, and is torn into mutually misaligned rings in the region, where the tidal precession torques are stronger than the local viscous torques. We derive the tidal-warp and tearing radii of the misaligned circumbinary disks around eccentric SMBH binaries. We find that in disks with the viscosity parameter α larger than a critical value depending on the disk aspect ratio, the disk warping appears outside the tearing radius. This condition is expressed for small amplitude warps as α > √H/(3r) for H/r∼<0.1, where H is the disk scale height. If α < √H/(3r), only the disk tearing occurs because the tidal warp radius is inside the tearing radius, where most of disk material is likely to rapidly accrete onto SMBHs. In warped and torn disks, both the tidal-warp and the tearing radii most strongly depend on the binary semi-major axis, although they also mildly depend on the other orbital and disk parameters. This strong dependence enables us to estimate the semi-major axis, once the tidal warp or tearing radius is determined observationally: for the tidal warp radius of 0.1 pc, the semi-major axis is estimated to be ∼10{sup −2} pc for 10{sup 7} M{sub ⊙} black hole with typical orbital and disk parameters. We also briefly discuss the possibility that central objects of observed warped maser disks in active galactic nuclei are supermassive black hole binaries.
The surroundings of the Milky Way globular cluster NGC 6809
ABSTRACT We study the outer regions of the Milky Way globular cluster NGC 6809 based on Dark Energy Camera observations, which reach nearly 6 mag below the cluster main-sequence (MS) turn-off. In order to unveil its fainter outermost structure, we built stellar density maps using cluster MS stars, once the contamination of field stars was removed from the cluster colour–magnitude diagram. We found that only the resulting stellar density map for the lightest stars exhibits some excesses of stars at opposite sides from the cluster centre that diminish soon thereafter at ∼ 0.32°.Studied globular clusters with apogalactic distances smaller than that of NGC 6809 (5.5 kpc) do not have observed tidal tails. The lack of detection of tidal tails in the studied inner globular cluster sample could be due to the reduced diffusion time of tidal tails by the kinematically chaotic nature of the orbits of these globular clusters, thus shortening the time interval during which the tidal tails can be detected. Further investigations with an enlarged cluster sample are needed to confirm whether chaotic and non-chaotic orbits are responsible for the existence of globular clusters with tidal tails and those with extra-tidal features that are different from tidal tails or without any signatures of extended stellar density profiles.
Total ecosystem carbon stocks at the marine-terrestrial interface: Blue carbon of the Pacific Northwest Coast, United States
The coastal ecosystems of temperate North America provide a variety of ecosystem services including high rates of carbon sequestration. Yet, little data exist for the carbon stocks of major tidal wetland types in the Pacific Northwest, United States. We quantified the total ecosystem carbon stocks (TECS) in seagrass, emergent marshes, and forested tidal wetlands, occurring along increasing elevation and decreasing salinity gradients. The TECS included the total aboveground carbon stocks and the entire soil profile (to as deep as 3 m). TECS significantly increased along the elevation and salinity gradients: 217 ± 60 Mg C/ha for seagrass (low elevation/high salinity), 417 ± 70 Mg C/ha for low marsh, 551 ± 47 Mg C/ha for high marsh, and 1,064 ± 38 Mg C/ha for tidal forest (high elevation/low salinity). Soil carbon stocks accounted for >98% of TECS in the seagrass and marsh communities and 78% in the tidal forest. Soils in the 0–100 cm portion of the profile accounted for only 48%–53% of the TECS in seagrasses and marshes and 34% of the TECS in tidal forests. Thus, the commonly applied limit defining TECS to a 100 cm depth would greatly underestimate both carbon stocks and potential greenhouse gas emissions from land-use conversion. The large carbon stocks coupled with other ecosystem services suggest value in the conservation and restoration of temperate zone tidal wetlands through climate change mitigation strategies. However, the findings suggest that long-term sea level rise effects such as tidal inundation and increased porewater salinity will likely decrease ecosystem carbon stocks in the absence of upslope wetland migration buffer zones.
Orbital evolution of the Galilean satellites
The orbital motions of the Galilean satellites exert dramatic control over their physical properties (most notably Io's) through tidal heating. In turn, tidal dissipation in the satellites, as well as in Jupiter, has governed the evolution of the orbits and, in particular, of the Laplace resonance. If the system started out of the resonance and evolved into it, forced eccentricities would have increased with time. Hence, the tidal melting of Io and the cracking of Europa'a surface may have occurred relatively recently. This theory requires that Jupiter's tidal dissipation factor be greater than about two million, a rather low value (high rate of tidal dissipation) compared with most models of Jovian interior processes. Alternatively, the system may have started even deeper in the resonance than it is today, a scenario which is consistent with larger values of the tidal dissipation factor. This model, with its correspondingly large initial forced eccentricities, would imply (1) that Io melted early and fast, and may have remained molten with only a thin solid skin until the present and (2) that the water mantles of both Europa and Ganymede remained largely molten for considerably longer than Callisto did, but later froze as their eccentricities and tidal heating decreased.
Numerical simulations of the Ross Sea tides
Tidal currents below the floating Ross Ice shelf are reconstructed by using a numerical tidal model. They are predominantly diurnal, achieve maximum strength in regions near where the ice shelf runs aground, and are significantly enhanced by topographic Rossby wave propagation along the ice front. A comparison with observations of the vertical motion of the ice shelf surface indicates that the model reproduces the diurnal tidal characteristics within 20 percent. Similar agreement for the relatively weak semidiurnal tides was not obtained, and this calls attention to possible errors of the open boundary forcing obtained from global-ocean tidal simulations and to possible errors in mapping zones of ice shelf grounding. Air-sea contact below the ice shelf is eliminated by the thick ice cover. The dominant sub-ice-shelf circulation may thus be tidally induced. A preliminary assessment of sub-ice-shelf conditions based on the numerical tidal simulations suggests that (1) strong barotropic circulation is driven along the ice front and (2) tidal fronts may form in the sub-ice-shelf cavity where the water column is thin and where the buoyancy input is weak.
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.