Tidal data inversion: interpolation and inference

Initial efforts in applying inverse methods to studies of ocean tides have focused on making the best use of a small number of observations to map tidal fields in a large area. As such, inversion can be viewed as an objective analysis scheme which uses a dynamically appropriate spatial covariance, derived from the shallow water equations, to interpolate and smooth a sparse data set. Data from recent altimetry missions are not sparsely distributed relative to tidal wavelengths in the open ocean, apparently reducing the need for complicated dynamically based interpolation schemes. Altimetric data sets are also quite large, making application of rigorous inversion methods to global tidal modeling a challenging computational problem. We describe here a new iterative solution scheme which allows us for the first time to fit the full set of TOPEX/Poseidon cross-over differences. The resulting solution (TPXO.3) fits validation tide gauges significantly better than previous inverse solutions. TPXO.3 also reduces residual cross-over variances relative to other recent inverse and empirical solutions, particularly in shallow water where improvements are dramatic. With the new solution approach very significant improvements in global tidal models should be possible in shallow areas and in the vicinity of complex bathymetry, where high-accuracy tidal modeling remains a challenging problem. With the recent improvements in the definition of tidal elevations in the open ocean it should now also be possible to resolve some long unanswered questions about tidal energetics and dynamics. Inverse methods provide a natural framework for addressing these issues, and making inferences about tidal dynamics. In particular, by bringing data and dynamics together in a single solution, we can rigorously test the consistency of the two. We present results of global and local inversions which suggest that over elongated bathymetric features oriented perpendicular to tidal flows, energy dissipation in the open ocean is significantly enhanced, presumably due to conversion of barotropic tidal motions into baroclinic modes. For the M₂ tide our preliminary results suggest that perhaps as much as 0.5 TW of energy is dissipated in this manner. However, due to the simplified linear dynamics and limited spatial resolution used for our inversion, there are significant uncertainties associated with these results. A more careful application of inverse methods to make more rigorous inferences about tidal energetics, including use of more reasonable prior dynamics, and the highest possible spatial resolution, should allow for closure of the tidal energy budget within the next few years.     

Assimilation of altimetry data for nonlinear shallow-water tides: Quarter-diurnal tides of the Northwest European Shelf

Non-linear tidal constituents, such as the overtide M₄ or the compound tide MS₄, are generated by interaction in shallow seas of the much larger astronomically forced “primary” tidal constituents (e.g., M₂, S₂). As such, errors in modeling these “secondary” shallow-water tides might be expected to be caused first of all by errors in modeling the primary constituents. Thus, in the context of data assimilation, observations of primary-constituent harmonic constants can indirectly constrain shallow-water constituents. Here we consider variational data assimilation for primary and secondary tidal constituents as a coupled problem, using a simple linearized perturbation theory for weak interactions of the dominant primary constituents. Variation of the resulting penalty functional leads to weakly non-linear Euler–Lagrange equations, which we show can be solved approximately with a simple two-stage scheme. In the first stage, data for the primary constituents are assimilated into the linear shallow water equations (SWE), and the resulting inverse solutions are used to compute the quadratic interactions in the non-linear SWE that constitute the forcing for the secondary constituents. In the second stage, data for the compound or overtide constituent are assimilated into the linear SWE, using a prior forced by the results of the first stage. We apply this scheme to assimilation of TOPEX/Poseidon and Jason altimetry data on the Northwest European Shelf, comparing results to a large set of shelf and coastal tide gauges. Prior solutions for M₄, MS₄ and MN₄ computed using inverse solutions for M₂, S₂, and N₂ dramatically improve fits to validation tide gauges relative to unconstrained forward solutions. Further assimilation of along-track harmonic constants for these shallow-water constituents reduces RMS differences to below 1 cm on the shelf, approaching the accuracy of the validation tide gauge harmonic constants.     

一种基于真实身份的BBS系统实名保障技术

用户身份的真实性一直是BBS系统管理的重要方面之一。采用SAML协议,将跨域单点登录中的认证技术引入到BBS系统中,从而实现了用户采用真实身份登录BBS系统,保证了BBS用户的实名。并以多个高校的BBS系统作为样例,建立起基于真实身份的示范BBS系统。     

Entrepreneurial advantages and disadvantages of belonging

The article analyzes the influence of religious network structures on entrepreneurial success. Members of the religious community of the Bohras in Tanga, Tanzania, are contrasted with entrepreneurs of other ethnic origins. It is shown that the religious network provides, through a loan scheme, the opportunities to start and run a business successfully. In this respect, the importance of the Islamic business ethic is underlined. Finally, the macro-economic effects of the network are outlined. This revised version was published online in July 2006 with corrections to the Cover Date.     

Versuch einer meeresmorphologischen Deutung von Satelliten-Luftbildern

Zusammenfassung Während man schon seit einiger Zeit Satelliten-Luftbilder für Festlandsbereiche interpretierte, nahm man allgemein an, daß die Meere auf diesen Bildern von einem einheitlichen und undifferenzierten Schwarz wiedergegeben würden. Es stellte sich aber heraus, daß auf manchen Bildern im Bereich der Meere deutlich verschiedene Grautönungen zu erkennen sind, die die Vermutung aufkommen lassen, es könne hier ein primärer oder zumindest sekundärer Zusammenhang mit submarinen Strukturen bestehen und es müßten sich somit Satelliten-Luftbilder auch meeresmorphologisch auswerten lassen.Zur Prüfung dieser Möglichkeit wurden in der vorliegenden Arbeit aus einer Fülle von Aufnahmen 27 Satelliten-Luftbilder mit entsprechenden Seekarten und anderen Unterlagen verglichen. Es zeigten sich an einigen Stellen verblüffende Übereinstimmungen von gewissen Grautönungen mit bekannten submarinen Formen, während an vielen anderen Stellen zunächst nur unsichere Aussagen möglich sind. Vor allem läßt sich derzeit noch nicht entscheiden, ob und wieweit primäre oder sekundäre Zusammenhänge bestehen.Die zur Beurteilung der Satellitenbilder notwendigen technischen Angaben bezüglich des Aufnahme- und Übertragungsverfahrens werden kurz resumiert, ausführlicher wird darüber an anderen Stellen (vgl. Schrifttum) berichtet.Eine kritische Diskussion des Problems der Eindringtiefe von Licht in Wasser führte zu der Annahme, daß im Bereich des Sonnenreflexes größere Tiefen als bislang vermutet ausgeleuchtet werden und sich aus der Zusammenschau aus großer Höhe veränderte optische Bedingungen ergeben können, als wir sie gewohnt sind.Insgesamt sprechen die Ergebnisse dafür, daß die Aussagefähigkeit der Methode noch an technischen Mängeln und dergleichen leidet, im Prinzip aber doch neue Beiträge zur Ozeanographie erwarten läßt.

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Essay of an ocean-morphological interpretation of Satellite-air-Pictures

Summary While for some time, Satellite-air-Pictures have already been interpreted for evaluation in the continental sphere, it was generally assumed that the oceans in such pictures were shown in an uniform and undifferentiated black colour. However, it was concluded that on some of these photos, showing the oceans, greyish shades were clearly visible which fact led to the assumption that one is confronted here primarily or, at least, secondarily by a coherence with submarine structures and, therefore, Satellite-air-Photos could perhaps also be construed in an ocean-morphological way.In order to test such a possibility, 27 Satellite-air-Photos out of a lot of pictures have been compared with the respective sea-charts and other data. In some instances, amazing conformities of certain greyish hues with the known substratal forms got visible, while in many other spots, so far, only vague statements can be made. First of all, at this point, it cannot as yet be decided whether and how far a primary or secondary context exists.The necessary technical data for the evaluation of such Satellite-air-Photos, with reference to the receiving and transmitting procedures, will be summarized in short, yet reports in greater detail can be found in the comparable literature.A critical discussion of the problems of depth of light-penetration into the water led us to the assumption that in the sphere of sunreflexes greater depths than so far presumed can be reached and, by the synoptical view from enormous heights, completely changed optical conditions may result, than we are so far used until now.Altogether, the results prove that the capacity of this method is still suffering from technical shortcomings, principally however, new contributions to oceanography can be expected.

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Essai d'une exploitation des images par satellites pour la morphologie marine

Résumé Tandis que depuis quelque temps déjà on interprétait des images par satellites de zones continentales, il était admis en général que les mers, sur ces images, seraient rendues par un «noir» uniforme sans nuances. Mais en fait, sur plus d'une image, on peut reconnaître distinctement dans les zones maritimes diverses tonalités de gris qui donnent à penser qu'il pourrait y avoir là une relation de premier ou tout au moins de second ordre avec des structures sous-marines. Dans ces conditions des images par satellites devraient offrir un intérêt pour la morphologie marine.Afin de vérifier cette possibilité, dans la présente étude, on a comparé 27 images par satellites, tirées d'un grand nombre de prises de vues, avec les cartes marines correspondantes et d'autres documents. En quelques points apparuent des concordances surprenantes entre certains tons de gris et des formes sous-marines connues, tandis qu'en beaucoup d'autres endroits on ne peut encore rien préciser pour le moment. Avant tout, en l'état actuel des choses, on ne peut encore affirmer qu'il existe — et dans quelle mesure — des concordances d'ordre primaire ou secondaire.Les données techniques nécessaires pour l'appréciation des images par satellites en ce qui concerne les procédés de prises de vue et de transmission, sont résumées succinctement; elles sont traitées de façon plus détaillée ailleurs (voir bibliographie).Une discussion critique du problème de la profondeur de pénétration de la lumière dans l'eau, permet de supposer que dans la zone où pénètre la lumière solaire, des profondeurs plus grandes que celles admises jusqu'alors sont éclairées et aussi que de la «vue d'ensemble», de haute altitude, peuvent résulter des conditions optiques qui diffèrent de celles auxquelles nous sommes accoutumés.Dans l'ensemble les résultats montrent que les informations à attendre de la méthode, souffrent encore d'un insuffisance de moyens techniques et autres mais laisse entrevoir, en principe, de nouvelles contributions à l'océanographie.