Approximation of the estimate error covariance function: Verification of the accuracy and generalization for the case of cross-covariance functions

Generalization of the approximation for the autocovariance function of estimate error, used frequently in four-dimensional analysis of the ocean's hydrophysical fields, is suggested for cross-covariance functions. It is shown that the principal properties of the covariance function of error estimate are not then violated. Approximation accuracy is studied through numerical experimentation using the two-dimensional equation for passive admixture transport as an example.Translated by V. Puchkin.     

Laboratory wave reflection analysis using co-located gages

Most coastal and ocean engineering laboratories employ techniques that use two or three spatially separated wave gages to estimate reflection of irregular waves in two-dimensional wave flumes. This paper presents a frequency domain method for separating incident and reflected wave spectra from co-located gages (gages located on the same vertical line). The technique is based on linear wave theory, and it can be applied to time series of sea surface elevation and horizontal water velocity collected in a vertical array, or it can be used with horizontal and vertical water velocity time series collected at the same point in the water column. Application of the method is limited to those frequencies showing good coherence between time series signals. Outside the range of good coherence, gross inaccuracies occur.The utility of the co-located gage method is illustrated using water velocity data collected in a wave flume with a laser Doppler velocimeter, and the method is validated for the case of complete reflection by a vertical wall. Side-by-side comparison to the spatially-separated wave gage method of Goda and Suzuki (1976) exhibited close agreement for a variety of irregular wave trains being weakly reflected by a mild sloping beach. The co-located gage method is useful in situations where there are spatial variations in the wavelength, such as on a mildly sloping bottom, or in the region close to highly reflective structures where errors arising from spatial variations in characteristic wave parameters would corrupt estimates made using the spatially-separated wave gage method.     

Measuring run-up on a natural beach

Field experiments have been performed to evaluate and intercompare two techniques for measuring run-up on natural beaches, resistance wires and films. Simultaneous deployment of wire sensors shows a low error (< 5%) in electronics gain, but a strong sensitivity to the elevation of the wires above the beach face. On a low slope (β ～ 0.02) beach, with incident wind waves of moderate height (H ～ 1 m), differences of only a few cm in the wire elevation cause variance differences as large as 25%, in otherwise identical sensors. Replicate digitizations of the same run-up film show variance differences as large as 20%, with an average deviation from the mean variance of 8%.Use of the film and resistance wire sensors on the same run-up field showed small differences in the mean swash elevation (i.e., set-up), but an 83% difference in swash variance. Much further work is needed to determine the dependence of sensor differences on beach slope, porosity, camera elevation and other factors.     

Mass flux and undertow in a surf zone

The mass of water carried shoreward by the breaking waves in a surf zone will, in a two-dimensional situation, be compensated by a seaward return flow, the undertow. It is shown that the undertow is driven by the local difference between radiation stress and the set-up pressure gradient which only balance each other in average over the depth. Turbulent shear stresses are required to maintain a steady situation. Comparison with measurements confirms the theoretical results.     

Spatial and temporal variability of crustal magnetization of a slowly spreading ridge: Mid-Atlantic Ridge (20°–24° N)

The results of the two- and three-dimensional magnetic inversions performed on data located between 20°–24° N on the Mid-Atlantic Ridge indicate the crustal magnetization has decayed exponentially for the last 10 Ma, and that this decay has been fairly symmetric about the ridge axis. After removal of the mean temporal decay, the residual field is characterized by more positive magnetizations at the second-order discontinuities, regardless of initial magnetization direction. A model that involves the preferential emplacement of serpentinized lithologies near the discontinuities is proposed to explain this correlation. The temporal detrending method also indicates that several ridge-parallel depressions located on the flanks of the ridge axis are regions of more positive magnetizations. These bathymetric depressions may mark the locations of detachment faulting that occurred during amagmatic periods of extension. The general symmetry of the crustal magnetization about the ridge axis does not support the occurrence of continuous detachment faulting proposed to correspond to the inner and outer corners of ridge axis discontinuities.     

Carbon-isotope composition of sediments from the Gulf of Papua

Rivers draining into the Gulf of Papua (GOP) from the Papua New Guinea mainland deliver approximately 340 × 10⁶ t yr^–1 of sediment to the marine environment. The terrestrially derived sediment contains 1.1 ± 0.2% particulate organic carbon with a carbon-isotope composition of –26.5 ± 0.2, and amounts to 3.7 ± 0.7 × 10⁶ t yr^–1. The carbon-isotope composition of sediments in the Gulf of Papua indicates that 40% of the sediment cover contains 75% or more terrestrially derived carbon. Suspended sediments that are transported beyond the delta complex of the Fly River are transported north and northwest, augmented by sediments from other rivers along the coast of the GOP. The carbon-isotope results suggest that a significant quantity of terrestrially derived sediment escapes from the GOP, either along the coastlines to east and west or into the deep ocean via the Moresby and Pandora troughs. Little sediment travels south onto the Great Barrier Reef shelf. Extrapolating the results from this study to the region of Oceania suggests a total flux of particulate organic carbon to the world's oceans from the islands of Oceania of ~ 90 × 10⁶ t yr^–1 or twice the flux of riverine POC from the major rivers of North America, South America, and Africa combined. While such a calculation must be considered illustrative only, the similar tectonic, geomorphologic, and climatic features of the islands of Oceania suggest that the calculation is unlikely to be grossly in error and that the rivers of Oceania therefore represent a major but poorly documented source of sediment and organic carbon to the global ocean.