The statistics of second order wave forces

A starting point in the statistical analysis of the slow drift motions of moored offshore structures is the determination of the statistical distribution of the second order exciting forces. In the past^2,6 an exponential probability density function has been used, this being the limiting case as the incident seastate becomes infinitely narrow banded. In the present note the second order force distribution is found for a general seastate and a significant deviation from an exponential distribution is found for those seastates which are likely to occur in practice. The statistical theory is based on a heuristic approximation to the second order force, which is shown to be consistent with a frequently used frequency domain approximation which has been suggested by Newman.⁸ Although Roberts² has shown that for very lightly damped systems the response statistics are independent of those of the exciting force, the present results may have a significant effect on the response statistics for higher levels of damping.     

The linearisation of three dimensional drag force in random seas with current

A frame invariant linearisation method for three-dimensional drag force in random seas with current is presented. Numerical results are compared with those obtained from a commonly used linearisation method which is based on a non-frame invariant approximation to the drag force. Significant differences are discovered and the present method is found to show closer agreement with computed time histories of the true drag force.     

A statistical analysis of non-linear random waves

A statistical analysis of unidirectional non-linear random waves is presented which is based on second-order random wave theory. The analysis technique is similar to a method which is available for the statistical analysis of a two-term Volterra series. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and eigenvectors of two real symmetric matrices, from which the cumulants, the characteristic function, and the probability density function of the surface elevation can be found. Various numerical examples are considered, and the possibility of extending the technique to deal with spreading seas is discussed.     

Random dynamic analysis of multi-body offshore structures

A general method for the dynamic analysis of multi-body offshore structures is presented, being based on a constraint matrix approach. A method of deriving the constraint matrix for a general structure is given, and this is then used to derive the equations of motion of a whole system from those of it's component parts. The response of the system to both first and second order random wave forces is found and then used to calculate the forces and moments in the connecting mechanisms. The structure is assumed to have rigid component parts and a linearised frequency domain analysis method is used, although other methods are discussed. To illustrate it's use, the method is applied to both the SBS and Yoke-CALM design of offshore mooring terminal.     

On the calculation of extreme wave heights: A review

Over the past two decades there has been a great deal of interest in calculating design waves for offshore structures. This paper reviews the data limitations, statistical assumptions, distributions, fitting methods, and statistical tests used to determine confidence intervals and goodness of fit. Use is made of an illustrative example from the Grand Banks of Canada to indicate how a design wave could be calculated. It is concluded that no single method will be entirely suitable for all data sets.     

On the accuracy of the GPS L2 observable for ionospheric monitoring

The introduction of the unencrypted global positioning system (GPS) L2 civil (L2C) signal has the potential to improve measurements made with the L2 frequency, an important observable in GPS-based ionospheric research and monitoring. Recent work has shown significant differences between the legacy L2P(Y) and L2C-derived total electron content rate of change index (ROTI). This difference is observed between L2P(Y) and L2C-derived ROTI with certain receiver models and between zero-baseline receiver pairs. We discuss the likely cause for these differences: L1-aided tracking used to track both the L2P(Y) and L2C signals. We also present L2C data that are confirmed to be from tracking independent of L1. Using the ionospheric-free linear combination, we show that the independently tracked carrier phase dynamics are significantly more accurate than the L1-aided observables. This result is confirmed by comparing the behavior of the L2C and L2P(Y) carrier phase observables upon a sudden antenna rotation.     

Variability of temperature,salinity and tidally‐averaged density in the middle estuary of the St Lawrence

Abstract

Surveys in the Middle Estuary of the St Lawrence have yielded a data base consisting of more than 15,000 T‐S pairs distributed over 62 13‐h profiling stations. Although the T‐S curves at each station are remarkably linear, the variability of the slopes and intercepts of the lines is considerable. The means and standard deviations of the temperature and salinity at each individual station are not explicable in terms of linear combinations of the parameters for location in the Estuary, the upstream water properties, the phase of the spring‐neap cycle and the tidal energies.

It is shown that the tidally‐averaged density structure is separable into horizontal and vertical components and that its vertical variation over the whole Estuary may be explained by any one of three different functional forms. However, its horizontal variation is not explicable in terms of linear combinations of the parameters mentioned in the paragraph above.

Plots of the horizontal variations in temperature, salinity or density may only be meaningful if the data are collected synoptically, and even then cannot be considered to be accurate over time‐scales longer than one tidal cycle.     

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.     

Evidences of Holocene transgression on Domingos Petrolini Swamp, southern coastal plain, Rio Grande do Sul, Brazil

The Domingos Petrolini Swamp, located on the Southern Coastal Plain of Rio Grande do Sul, near the town of Rio Grande, constitutes an ample holocene lagoonal deposit. Events related to the holocene transgression and their diverse phases of glacial-eustatic ocillations were found through palynological analysis. Bases on these palynological data, four distinct phases to the paleoenvironmental evolution of the ecosystem were identified. It has also shown a transgressive restricted marine sequence on the base , which suggests the existence of a coastal brackish lagoon or a marisme type of environment. Later, there was a gradation for continentality conditions along with a scarce pollinical record. The third phase is characterized by the presence of marine components and halophyte vegetation, showing another transgressive event in that place. Lastly, the end of direct marine influence over the swamp was recorded and also the vegetation development as it appears these days.