A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents

Spatially distributed sea wave measurements

In recent years, there has been growing interest in remote and proximal observation of sea surface waves. This has been partially driven by new technologies allowing the characterization of wave fields in both their spatial and temporal aspects. Typical examples are radar systems and stereo-imaging that permit remote monitoring of oceanic waves (from satellites, platforms, or vessels) with remarkable accuracy and range of use. These new exciting possibilities usually come at the price of being relatively harder to master with respect to traditional “point-like” approaches providing measurements limited to a temporal perspective. This difficulty is not restricted to the technology itself (see, for example, the delicate camera-calibration process required in stereo-imaging) but also on how to properly process, analyze, and assimilate spatio-temporal data. Therefore, in this Special Issue, we decided to embrace a wide range of topics that have led a multitude of multi-disciplinary works in the recent past, including: Wave mechanics and sea surface dynamics; Analysis of the wave climate and its extremes; Data fusion and signal processing; Statistical and probabilistic methods; Assessment of wave models. We did our best to propose recent advancements, not only on the technological aspect of spatially distributed sea waves acquisition but also on the characterization of wave statistics from measured and assimilated data. For the former aspect, we included the work of Vieira et al. [1], proposing the first cheap and simple stereo-based technique to estimate the 3D sea surface elevation from inexpensive smartphones. For the latter, the paper of Serebryany et al. [2] investigates internal waves on a narrow steep shelf of the northeastern coast of the Black Sea using the spatial antenna of line temperature sensors. We also included a discussion on space-time wave extremes in the paper of Benetazzo et al. [3] and a comparison of assimilated coastal wave data by Yukiharu Hisaki [4]. Finally, the work of Ciurana and Aguilar [5] provides an overview of how an ensemble of meteorological buoys and citizen science data can help economic activities to achieve optimal performances (in a case study, to predict optimal surfing days in the Iberian Peninsula). We hope that these works will be interesting both for researchers already working on this topic and for those who want to embrace the new possibilities offered by modern sea wave acquisition techniques

Short-Term/Range Extreme-Value Probability Distributions of Upper Bounded Space-Time Maximum Ocean Waves

There is general consensus that accurate model predictions of extreme wave events during marine storms can substantially contribute to avoiding or minimizing human losses and material damage. Reliable wave forecasts and hindcasts, together with statistical analysis of extreme conditions, are then of utmost importance for monitoring marine areas. In this study, we perform an analysis of the limitations of the available short-term/range extreme-value distributions suitable for space-time maximum wave and crest heights. In particular, we propose an improvement of the theoretical distributions by including upper bounds on the maximum heights that waves may reach. The modification of the space-time probability distributions and its impact for extreme-value assessment is discussed in the paper. We show that unbounded space-time distributions are still effective provided that the surface area included in the analysis has sides smaller than O(102 m). For wider surfaces, the use of the bounded distributions is consistent with the expected saturation of maximum heights that ocean waves attain

GLI EFFETTI DELL’ANNULLAMENTO DELL’AGGIUDICAZIONE SUL CONTRATTO MEDIO TEMPORE STIPULATO

The doctorate thesis assigned to me deals with the problem of the effects of cancelling the tender procedure of a call for tenders on the contract stipulated in a judicial capacity in the course of the proceedings between the administration and the company, which turns out to have been unlawfully selected. As regards this question, the case law and legal theory have outlined solutions in terms of interpretation which are at two completely different ends of the spectrum (referring to the retractability, nullity and null and void agreement of the contract respectively) and which induces a set of questions regarding substantive and procedural law. The whole issue concerns the relations between the tender procedure and contract and the majority of the debate in fact centres on the nature (procedural or contractual) of the deed of adjudication. In order to correctly set out this research I therefore decided to dedicate the first part of the work to the problem of the nature of the deed of adjudication. In carrying out a similar survey, I deemed it necessary to take the steps from the traditional guidance that asserts the concurrence, in the tender procedure, of two deeds (even though they are formally separated in the procedure): an investigation (declaratory) deed (administrative), whereby the final deed of the selection procedure of the contractor is finalised, which consists of verifying the best offer; and a private contractual deed, which contains the agreement declaration of the public administration with regard to the contract to be stipulated. I focused in particular on the normative grounds of this theory (in particular, on the principle of equivalence of the record of the adjudication for the contract sanctioned by art. 16, paragraph 4, of the R.D. no. 2440/1923 and on the scope of this provision); and thereby making use of the specifications provided by the case law over time and the contributions made by legal theory. I subsequently analysed the concept of the tender procedure solely in terms of an administrative act, sustained by a minor part of the legal theory and case law, but which was endorsed by the Italian Supervisory Authority for Public Works with the decision dated 2 October 2002, no. 24, as it stands it is based on an unconvincing interpretation of the regulations regarding public works and those which provide for the non-conclusive nature of the tender procedure. With regard to the problem in question, I was also able to observe how the new Public Contracts Law, approved with the Italian Legislative Decree 12 April 2006, no. 163, does not contribute towards clarifying the point. If in truth on the one hand, this appears to sanction the overcoming of the traditional planning, according to which the record of the adjudication is equivalent to the contract, expressly asserting, in art. 11, paragraph 7, that “the tender procedure is not equivalent to the acceptance of the offer,” on the other hand, the new law reproduces – in art. 11, paragraph 9 – provision (art. 109, paragraph 3, of the D.P.R. no. 554/99), which seems instead allow an interpretation to the contrary and therefore to confirm the traditional planning, according to which the record of the adjudication takes the place of the contract. As regards the results achieved at the end of the survey on the nature of the tender procedure, from this point of view I decided that the conclusions should be shared. This is where that case study orientation came from, which constitutes the specification of the traditional theory of the dual nature of the tender procedure. This differentiates from the deed of adjudication in terms of content in relation to the type of procedure followed and, in particular, excludes the contractual value of the tender procedure (and therefore sustains the need to proceed to a separate, subsequent stipulation) if the proceedings of the private negotiation and the competitive tender have been followed. After having examined the essential character and nature of the tender procedure, I focused on the specific topic of the doctorate thesis (the effects of cancelling the tender procedure on the stipulated mid-term contract), moving from a (critical) analysis of the main guidelines of civil case law and legal theory recorded on the topic. From this point of view, I examined, first of all, the traditional and oldest guidelines of ordinary civil law, which asserts that the contract stipulated on the basis on an unlawful tender procedure can be cancelled in accordance with art. 1441 of the Italian Civil Code (hereafter c.c.). It is believed that this retractability can only and exclusively be asserted by the public administration, the only body that can legitimately carry out the relative act in conformity to the cited art. 1441 c.c.. From this perspective, I dedicated particular attention to the different reconstructive hypotheses that were elaborated regarding the theory of retractability concerning the contract (retractability due to the public administration’s inability negotiate, former art. 1425, first paragraph of the c.c.; retractability due to errors the agreement, former art. 1427 and foll. of the c.c.; retractability due to the public administration’s error in contractual validation). I then went on to examine the theory, also strongly represented in legal theory and foll. and case law, which brings back the condition of the tender contract stipulated based on a tender procedure cancelled in a judicial capacity with hypothetical absolute nullity, in accordance with art. 1418 of the c.c., concentrating especially on the theory of structural nullity due to a lack of agreement former art. 1418, paragraph 2, and 1325, no. 1, of the c.c. and on the nullity theory due to the violation of binding regulations former art. 1418, first paragraph of the c.c.. After having examined the different positions taken in the civil sphere, I devoted my attention to studying the “giuspubblicistica” position on the relationship between cancellation and contract, also through the (critical) analysis of the most significant case law rulings on the topic. I paid special attention to the theory of the automatic null and void agreement, which asserts the inefficiency of the contract following the cancellation of the tender procedure on the presupposition of the existence of a link of necessary consequentiality between the public representation procedural sequence and the (subsequent) stipulation of the contract and the relative inefficiency that has occurred, according to which the inefficiency of the contract would not be produced automatically, but following the judicial initiative of the omitted contractor and notwithstanding the rights acquired by bona fide third parties, in application of art. 23, paragraph 2, and 25, paragraph 2 of the c.c.. At the end of the close examination I analysed the advantages and limitation of the various reconstructions proposed, with special attention paid to the criticisms directed at these theories. With particular regard to the traditional theory of the retractability of the contract, I pointed out that on the one hand – reserving the validation to request the cancellation of the contract to the only subcontracting organisation – it seems to adequately satisfy the needs of certainty of the judicial relations, on the other hand this concept does not appear to guarantee the third party in the same way, which has obtained the cancellation of the contract documents, nullifying in such a way the protection achieved by the latter in an administrative judicial capacity. I also ascertained how the theory of retractability appears to be inspired by an ‘artificial’ distinction between the administrative selection stage of the contractor and the strictly contractual period of the issue (which is clarified when stipulating the contract). Indeed, as I was able to notice in specifically examining the problem of the nature of the tender procedure, it cannot be the case that the two stages cannot always be clearly separated, having considered that the tender procedure in some cases could also be regarded as a declaration of contractual agreement by the public administration as regards the contract to be stipulated and the subject with which to conclude the contract. For this reason it seems difficult to sustain that the cancellation of the tender procedure cannot ever weigh upon the efficiency of the negotiation, and that is to say regardless of an explicit ruling of cancellation of the contract by the ordinary court, as the supporters of the theory of retractability believe. As regards the theory of nullity of the contract, I pointed out how this has been criticised above all as the actual result of an original fault in the contract (which characterises the scheme of radical invalidity) is attributed to an event that has taken place (the cancellation of the tender procedure), with unacceptable consequences (on the level of certainty of the judicial relations), such as the exposure of the same contract to the verification of its office nullity, with any prescriptive limitations and by anyone concerned with them. Finally, as regards the recent reconstructions of administrative case law, substantially referring to the inefficiency of the contract, I was able to indicate how the same, although the interests in play have the merit of completely assessing, giving the right importance to protecting the rights of bona fide third parties, lead to results which are partly reassuring concerning the compatibility of this kind of reconstruction with the system coordinates. In conclusion, I was able to ascertain the deficiency of the various theories examined in explaining the problem of the effects of cancelling the tender procedure on the contract. This inadequacy seems to come mainly from the lack of consideration – by these theories – of the problem of the (procedural and/or contractual) nature of the tender procedure itself and the relations between the tender procedure and contract. I therefore attempted to identify a prospective solution suitable for resolving the problem of the relationship between the invalidity of the public tenders procedure and contract in light of the close examination of the various theories shown by the legal theory and case law (retractability; nullity; automatic null and void agreement; the relative inefficiency that has occurred), reaching a range of conclusions according to the legal, contractual or only procedural description, which we would like to attribute to the deed of adjudication. From this point of view I hypothesised that when the deed of adjudication also takes on contractual worth, the cancellation of the tender procedure causes the nullity of the stipulated mid-term contract, without the need for constitutive statements of its ceased effect, whereas in the cases in which the tender procedure, subject to cancellation, only holds procedural value, the contract must only be deemed as retractable. The combination of the surveys described so far lead to the drafting of three chapters of the doctorate thesis. The first of which is dedicated to the problem of the nature of the tender procedure. The second chapter concentrates on the analysis of the positions of the civil case law and legal theory as to the types of the stipulated mid-term contract. The third chapter focuses on the analysis of the theories of administrative case law and the identification of a prospective solution to the problem

Weak Statistical Constraints for Variational Stereo Imaging of Oceanic Waves

We develop an observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states via a variational stereo method. In the context of active surfaces, the shape and radiance of the wave surface are obtained as minimizers of an energy functional that combines image observations and smoothness priors. To obey the quasi Gaussianity of oceanic waves observed in nature, a given statistical wave law is enforced in the stereo variational framework as a weak constraint. Multigrid methods are then used to solve the partial differential equations derived from the optimality conditions of the augmented energy functional. An application of the developed method to two sets of experimental stereo data is finally presented