The interpretation of stable isotopes in deep-sea sediments: An error analysis case study

Stable oxygen isotope records are widely used in paleoceanographic and paleoclimatic studies. These records are subject to measurement and sampling errors as well as distortions from benthic mixing and nonlinear sedimentation. The magnitudes of these various errors are examined in this paper using an equatorial Pacific piston core record through Termination II. Measurement precision can be improved by increasing the sample size or by averaging the results from replicate analyses. Benthic mixing parameters and sedimentation rate history are important when a stratigraphic record is used to reconstruct original oceanographic and climatic signals. Obtaining an upper limit on the thickness of the benthic mixed layer is the most important concern in keeping processing noise small. Mixed layer thickness can be estimated in a variety of ways, including radiocarbon dating and the use of ash and tektite layer profiles. Sedimentation rate history can be determined in box cores by radiocarbon dating, but is difficult to constrain in older records. Uncertainties in the benthic mixing parameters and sedimentation rate history combine with measurement error to yield a large envelope of interpretive uncertainty around any measured isotope signal.     

Doppler radar radial winds in HIRLAM. Part II: optimizing the super-observation processing

Doppler radar radial wind observations are modelled in numerical weather prediction (NWP) within observation errors which consist of instrumental, modelling and representativeness errors. The systematic and random modelling errors can be reduced through a careful design of the observation operator (Part I). The impact of the random instrumental and representativeness errors can be decreased by optimizing the processing of the so-called super-observations (spatial averages of raw measurements; Part II).
The super-observation processing is experimentally optimized in this article by determining the optimal resolution for the super-observations for different NWP model resolutions. A 1-month experiment with the HIRLAM data assimilation and forecasting system is used for radial wind data monitoring and for generating observation minus background (OmB) differences. The OmB statistics indicate that the super-observation processing reduces the standard deviation of the radial wind speed OmB difference, while the mean vector wind OmB difference tends to increase. The optimal parameter settings correspond at a measurement range of 50 km (100 km) to an averaging area of 1.7 km² (7.3 km²).
In conclusion, an accurate and computationally feasible observation operator for the Doppler radar radial wind observations is developed (Part I) and a super-observation processing system is optimized (Part II).     

Mitigating horizontal divergence “checker-board” oscillations on unstructured triangular C-grids for nonlinear hydrostatic and nonhydrostatic flows

A complication of finite-volume triangular C-grid methods is the numerical emergence of horizontal divergence errors that lead to grid-scale oscillations in vertical velocity. Nonlinear feedback via advection of momentum can lead to numerical instability in velocity modes via positive feedback with spurious vertical velocities induced by horizontal divergence truncation error. Existing strategies to mitigate divergence errors such as direct divergence averaging and increased diffusion do not completely mitigate horizontal vertical velocity oscillations. We present a novel elliptic filtering approach to mitigate this spurious error and more accurately represent vertical velocities via improved calculation of horizontal divergences. These results are applied to laminar curved channel flows, demonstrating the applicability of the method to reproduce secondary flow features.     

Analysis of a possible sea floor strain measurement system

Abstract

A logical approach to large area sea floor strain measurement is to use a set of precision acoustic transponders interrogated successively from a large number of different positions by a near‐bottom survey vehicle. Limiting errors in such an approach can be segregated into two classes implying two different scales on which averaging should be carried out. First are those arising from individual travel time and vehicle depth measurements. Second are those associated with imperfect knowledge of the sound propagation speed. The first are essentially independent from one measurement to the next; for the second, statistically independent observations must be separated by the order of 100 m. Several thousand observations of successive travel times to individual transponders would thus be smoothed to produce the equivalent of a smaller number (few hundred) of sets of simultaneous range observations, and then these sets would be used to determine the transponder array geometry. Computer simulations using realistic assumptions show that centimeter‐level accuracy can be achieved over areas several kilometers across.     

Temporal domain processing for a synthetic aperture array

A method for the synthesis of an aperture with improved bearing resolution and signal gain is described. The proposed method temporally synthesizes data from an overlap correlator, which is obtained by aperture domain averaging of phase differences. Previous studies, such as extended towed array measurements (ETAM), had a restriction in that the overlapped hydrophones between successive measurements of a towed array were required to have identical positions in space. In this paper, however, it is shown that the phase correction factors can be estimated without restriction on the positions of the overlapped hydrophones. This implies that the proposed method is able to utilize more snapshots to extend the towed array. Simulation results showed that the proposed method resulted in higher estimation accuracy than ETAM. In addition, the effects of coherency and other systematic errors on the proposed method were examined     

On the accuracy of current measurements by means of HF radar

The accuracy of surface current velocities measured by high-frequency (HF) radar is investigated. Data from the two radar systems of the University of Hamburg, CODAR (Coastal Radar) and WERA (Wellen Radar), are compared with in situ data. In one experiment, CODAR and a near-surface current meter were operated simultaneously over a 19-day period. In addition, WERA was operated for 6 days during that period. In the other experiment, WERA and a bottom-mounted current meter were operated simultaneously over a 35-day period. Both radars use frequencies of about 30 MHz where backscattering is due to ocean waves of 5 m wavelength. The influence of the orbital motion of underlying longer waves on radial velocity errors is investigated. In accordance with theory, the measured standard deviations of HF-measured current velocities depend on the sea state. Depending on the sea state, estimated errors range from 3 to 10 cm·s^-1 and explain only part of the rms difference of 10-20 cm·s^-1 found between HF and in situ current measurements. The rest is assumed to be due the differences of the quantities measured, e.g., the spatial averaging     

Swath bathymetry: principles of operation and an analysis of errors

The principles of swath bathymetry are described, and the main cause of depth error is identified as acoustic interference, particularly from the sea surface. An error analysis is presented which gives the relationship among depth errors, the signal-to-interference ratio, the grazing angle, receiver spacing, and area resolution. It permits a prediction of when its measurement of depth can meet the accuracies required for nautical charting. Ways of reducing multipath interference and of minimizing its effect when it does occur are discussed. Particularly important are area averaging, the use of widely spaced receivers with ambiguities resolved by the vernier technique, and phase tracking for avoiding bias problems     

Fast matched field processing

It is shown how the computational burden of source localization by matched field processing (MFP) can be significantly reduced (20 to 30 times) by expressing the correlation in terms of a discrete Fourier transform and using the fast Fourier transform (FFT) algorithm. The price paid to achieve increased speed is in the form of quantization phase errors. It is shown through analysis and computer simulation that the quantization errors reduce the source peak height, depending upon the size of DFT. The proposed fast MFP works for range localization only. However, the depth estimation is possible by repeated application of the above algorithm for different depths     

Performance comparison of high resolution bearing estimationalgorithms using simulated and sea test data

The performance of both the Capon and the MUSIC high resolution bearing estimation algorithms is investigated using both simulated data and sea test data collected with an experimental planar array. The major problem with these estimators is their sensitivity to both system errors and deviations from the assumed noise model. To alleviate this problem, two methods for preprocessing the data before they are input into the high-resolution algorithm are investigated: beam space and sector focused stability. The performance of both high-resolution estimators is examined, using both types of preprocessing, and the results are compared with those for the standard element-space (ES) techniques, assuming both finite cross-spectral-matrix (CSM) averaging errors and weakening target strengths. For the Capon estimator the performance is only superior to the standard element space technique when the CSM is calculated using a small number of averages. For the MUSIC estimator, both preprocessing techniques give clearly superior results over standard space techniques, with the SFS preprocessor performing the best     

Improving the Coastal Mean Dynamic Topography by Geodetic Combination of Tide Gauge and Satellite Altimetry

Abstract

The ocean mean dynamic topography (MDT) is the surface representation of the ocean circulation. The MDT may be determined by the ocean approach, which involves temporal averaging of numerical ocean circulation model information, or by the geodetic approach, wherein the MDT is derived using the ellipsoidal height of the mean sea surface (MSS), or mean sea level (MSL) minus the geoid as the geoid. The ellipsoidal height of the MSS might be estimated either by satellite or coastal tide gauges by connecting the tide gauge datum to the Earth-centred reference frame. In this article we present a novel approach to improve the coastal MDT, where the solution is based on both satellite altimetry and tide gauge data using new set of 302 tide gauges with ellipsoidal heights through the SONEL network. The approach was evaluated for the Northeast Atlantic coast where a dense network of GNSS-surveyed tide gauges is available. The typical misfit between tide gauge and satellite or oceanographic MDT was found to be around 9?cm. This misfit was found to be mainly due to small scale geoid errors. Similarly, we found, that a single tide gauge places only weak constraints on the coastal dynamic topography.     

Sediment transport patterns at Trafalgar offshore windfarm

A simple analytical model of wave propagation has been developed in order to study the potential sediment transport patterns due to the action of currents and waves in the neighborhood of cylindrical structures as well inside a group of these structures. The attention is focused on the study of Trafalgar offshore windfarm, a case in which it has been necessary to analyze the flow trough porous structures in order to model fish growing-cages planned to be installed at each aerogenerator structure. The results are obtained by averaging over one period of wave in order to evaluate the net potential sediment transport. The analysis of the results reveals how the processes of wave diffraction and reflection give rise to periodic patterns of sediment transport around and between the structures.     

Data assimilation with inequality constraints

If values of variables in a numerical model are limited to specified ranges, these restrictions should be enforced when data are assimilated. The simplest option is to assimilate without regard for constraints and then to correct any violations without worrying about additional corrections implied by correlated errors. This paper addresses the incorporation of inequality constraints into the standard variational framework of optimal interpolation with emphasis on our limited knowledge of the underlying probability distributions. Simple examples involving only two or three variables are used to illustrate graphically how active constraints can be treated as error-free data when background errors obey a truncated multi-normal distribution. Using Lagrange multipliers, the formalism is expanded to encompass the active constraints. Two algorithms are presented, both relying on a solution ignoring the inequality constraints to discover violations to be enforced. While explicitly enforcing a subset can, via correlations, correct the others, pragmatism based on our poor knowledge of the underlying probability distributions suggests the expedient of enforcing them all explicitly to avoid the computationally expensive task of determining the minimum active set. If additional violations are encountered with these solutions, the process can be repeated. Simple examples are used to illustrate the algorithms and to examine the nature of the corrections implied by correlated errors.     

The effect of phase-shifter errors on the performance of an antenna-array beamformer

The paper considers the random phase errors in the phase shifters which are used in an antenna array to steer the beam in the look direction, and analyzes the effect of these errors on the performance of the optimal processor which maximizes the output SNR by deriving the expressions for the output signal power, residual interference power, output SNR, and the array gain as a function of the variance of these errors. The paper also considers the phase quantization error which arises in the digital phase shifters and shows how the performance of the optimal processor depends on the number of bits of the digital phase shifters.     

Analysis of Phase Error Effects on Stripmap SAS

It is often of interest to consider how uncompensated platform motion can degrade the ideal point scatterer response (PSR) of a synthetic aperture sonar (SAS). This information can be used to shape the design of the sonar itself as well as that of the platform carrying it. Also, knowledge of how certain types of motion affect a SAS image can reduce the time spent in troubleshooting motion estimation and compensation schemes. In the field of spotlight-mode synthetic aperture radar (SAR), the effects of phase errors across the synthetic aperture are well documented (for example, Chapter 5 of Carrara , 1995). The counterpart problem for the stripmap mode is less well developed in the literature. This paper explores the effects of uncompensated phase errors on stripmap imagery and shows that, under certain conditions, they are similar to those for spotlight mode processing.      

Effects of cross-shore boundary condition errors in nearshore circulation modeling

The paper analyzes the effect which prescribed errors in the cross-shore boundary conditions for a computational domain along a beach have on the flow field predicted inside the domain. This problem is relevant because errors in boundary conditions are unavoidable when modeling limited domains of a nearshore region. For simplicity, we consider a longshore uniform plane beach with monochromatic, obliquely incident waves, and assume depth uniform currents. It is then studied analytically and numerically how small perturbations of the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. It is found that the errors at the upstream cross-shore boundary tend to spread over a long distance downstream of the boundary, while the influence of the errors in the downstream boundary condition is limited to the adjacent upstream area of the computational domain. Both the numerical and analytical solutions show that the errors introduced at the upstream boundary decay exponentially in the surf zone at a rate proportional to the bottom friction. A simple formula is developed to estimate the influence distance of the upstream errors. If we consider the mismatch in the volume flux at the upstream boundary, the error merely redistributes in the cross-shore direction to conserve volume. In the case of excessive flux or velocity specified at the cross-shore boundaries, a circulation cell tends to appear in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.     

CIAY MINERALS IN THE SURFACE SEDIMENTS OF THE BOHAI SEA

Analyses of clay mineralogy about 30 surface sediments indicate widespread occurrence of illite, kaolinite, chlorite and montmorillonite throughout the Bohai Sea. Illite is the most abundant mineral, averaging 60%, kaolinite, next to illite, is the most abundant one,averaging 18%. Chlorite and montmorillonite come second, averaging 12% and 10% respectively. The distributive patterns of clay minerals in the surface sediments are closely related to the suspended materials carried into the Bohai Sea, especially to those did by the Huanghe River, and to water dynamics in the area. Based on the distribution, the assemblages and the others of clay minerals, the Bohai Sea can be divided into two clay mineral regions, the Liaodong Gulf region and the Bohai-Laizhou Bay region.     

Microstructure of turbulence in the northern North Sea: a comparative study of observations and model simulations

Dissipation rate measurements in the northern North Sea from two independent observations are compared with various numerical models. The turbulence was characterised by tidal forcing in the bottom boundary layer and atmospheric forcing in the surface boundary layer. The observations were carried out by using free-falling profilers equipped with shear probes and fast CTD sensors. The models are based on Reynolds averaging and range from simple one-equation models to two-equation models with algebraic second-moment closures. Several error measures are applied for comparison of observations and model results. It is shown that the differences between the two observations are significantly larger than the equivalent measures between the model results. This is caused by the stochastic character of turbulent microstructure in connection with under-sampling, but also by the distance between the two observational sites, the movements of the vessels, instrument errors and so forth. The models on the other hand, although closed on different levels, are all based on the same assumptions and driven by the same external forcing, thus showing only relatively small differences between each other.     

Stereovision imaging on submersible platforms for 3-D mapping of benthic habitats and sea-floor structures

We investigate the deployment of a submersible platform with stereovision imaging capability for three-dimensional (3D) mapping of benthic habitats and other sea-floor structures over local areas. A complete framework is studied, comprising: 1) suitable trajectories to be executed for data collection; 2) data processing for positioning and trajectory followed by online frame-to-frame and frame-to-mosaic registration of images, as well as recursive global realignment of positions along the path; and 3) 3D mapping by the fusion of various visual cues, including motion and stereo within a Kalman filter. The computational requirements of the system are evaluated, formalizing how processing may be achieved in real time. The proposed scenario is simulated for testing with known ground truth to assess the system performance, to quantify various errors, and to identify how performance may be improved. Experiments with underwater images are also presented to verify the performance of various components and the overall scheme.     

Wind-wave generation of ocean current: on model identification

It is shown how stochastic models based on inertial fluctuations, forced by Stokes drift and wind stress, give apparently accurate predictions of sea surface current. A parameter estimation procedure that gives subjectively reasonable results may therefore also be found. However, objective model identification turns out to be difficult and an estimation model capable of following large-scale model errors is necessary for reasonably accurate parameter estimates. Such a model is proposed and simulation results are presented and discussed. In this mode the inertial oscillation damping, is easily overestimated and the Stokes drift effect is seen to be smaller than the wind stress effect. The latter appears to be uncertain     

Assessing the utility of frequency dependent nudging for reducing biases in biogeochemical models

Bias errors, resulting from inaccurate boundary and forcing conditions, incorrect model parameterization, etc. are a common problem in environmental models including biogeochemical ocean models. While it is important to correct bias errors wherever possible, it is unlikely that any environmental model will ever be entirely free of such errors. Hence, methods for bias reduction are necessary. A widely used technique for online bias reduction is nudging, where simulated fields are continuously forced toward observations or a climatology. Nudging is robust and easy to implement, but suppresses high-frequency variability and introduces artificial phase shifts. As a solution to this problem Thompson et al. (2006) introduced frequency dependent nudging where nudging occurs only in prescribed frequency bands, typically centered on the mean and the annual cycle. They showed this method to be effective for eddy resolving ocean circulation models. Here we add a stability term to the previous form of frequency dependent nudging which makes the method more robust for non-linear biological models. Then we assess the utility of frequency dependent nudging for biological models by first applying the method to a simple predator–prey model and then to a 1D ocean biogeochemical model. In both cases we only nudge in two frequency bands centered on the mean and the annual cycle, and then assess how well the variability in higher frequency bands is recovered. We evaluate the effectiveness of frequency dependent nudging in comparison to conventional nudging and find significant improvements with the former.