Optimal Spectral Decomposition (OSD) for Ocean Data Assimilation

Observational salinity data from the Global Temperature and Salinity Profile Program (GTSPP) are used to identify temporal and spatial variability of the upper ocean freshwater content (FWC). First, the optimal spectral decomposition (OSD) is used to build up monthly synoptic temperature and salinity data set from January 1990 to December 2009 on 1oA—1o grids and the same 33 vertical levels as the World Ocean Atlas 2005. Then, the monthly varying upper layer FWC fields (F) with four different layer thicknesses (surface to 50, 100, 300, and 700 m depths) are obtained.

We have compared and evaluated the water mass census in the Greenlend-Iceland-Norwegian (GIN) Sea area from climatologies, observational data sets and model output. The four climatologies evaluated were: the 1998 and 2001 versions of theWorld Ocean Atlas (WOA98, WOA01), and the United States Navy’s GDEM90 (Generalized Digital Environmental Model) and MODAS01 (Modular Ocean Data Assimilation System) climatologies. Three observational data sets were examined: the multidecadal (1965-1995) set contained on the National Oceanographic Data Center’s (NODC) WOD98 (World Ocean Data) CD-ROM, and two seasonal data sets extracted from observations taken on six cruises by the SACLANT Research Center (SACLANTCEN) of NATO/Italy between 1986-1989. The model data is extracted from a global model run at 1/3 degree resolution for the years 1983-1997, using the POP (Parallel Ocean Program) model of the Los Alamos National Laboratory. The census computations focused on the Norwegian Sea, in the southern part of the GIN Sea, between 10◦W-10◦E and 60◦N-70◦N, especially for comparisons with the hydrocasts and the model. Cases of such evaluation computations included: a) “short term” comparisons with quasi-synoptic CTD surveys carried out over a 4-year period in the southeastern GIN Sea; b) “climatological” comparisons utilizing all available casts from the WOD98 CD-ROM, with four climatologies; and c) a comparison between the WOA01 climatology and the POP model output ending in 1997. In this region in the spring, the fraction of ocean water that has salinity above 34.85 is ∼ 94%, and that has temperatures above 0◦C is ∼ 33%. Three principal water masses dominated the census: the Atlantic water AW, the deep water DW and an intermediate water mass defined as Lower Arctic Intermediate Water (LAIW). Besides these classes, both the climatologies and the observations exhibited the significant presence of deep water masses with T-S characteristics that do not fall into the “named” varieties, e.g., Norwegian Sea or Greenland Sea deep water (NSDW, GSDW). The seasonal volumetric changes for the Atlantic (AW), intermediate (LAIW) and deep waters (DW) in the GIN Sea are in reasonably good agreement between the climatologies, and with the results of hydrographic census surveys. Typical seasonal changes (spring-summer) involve about 30 × 103 km3 of AW increase and 33 × 103 km3 of LAIW decrease, and a decrease of about 32 × 103 km3 of DW between spring and autumn.

A numerical model, the Parallel Ocean Program (POP) was used to run a 46-year simulation of the North Pacific Ocean beginning in January 1960. The model had a horizontal resolution of 0.25°, 28 vertical levels, and employed spectral nudging that, unlike standard nudging, nudges only specific frequency and wavenumber bands. This simulation was nudged to the mean and monthly Levitus climatology of potential temperature and absolute salinity (SA). The model was forced with the mean monthly winds, sea level pressure, net heat flux, and precipitation from the National Centers for Environmental Prediction (NCEP).The simulation was used to examine the anomalous intrusions, previously observed from 2001 to 2002, of cooler and fresher (less spicy) water flowing southward along the coast of western North America. The simulated anomaly began in 1999 in the North Pacific, progressed southeastward towards the coast and then southward, at least as far south as southern California. The southward velocity signal, modulated by a strong annual cycle, reached Point Conception in 2000 while the temperature and SA anomalies arrived later, in 2002–03. The simulated velocity anomalies were eastward at about 3 cm s−1 in the northeast Pacific near 47°N in agreement with observations. Simulated coastal southward flow speeds reached 10–20 cm s−1 during the summer from 2000 to 2002.This intrusion was by far the largest to occur over the entire length of the simulation. It was also the only time during the simulation when the Victoria mode was positive (associated with enhanced flow to the east via the North Pacific Gyre Oscillation (NPGO)) and the Multivariate El Niño-Southern Oscillation (ENSO) Index (MEI) was negative (La Niña conditions), tending to cause a southward flow anomaly along the coast.

A regional ocean model was used to simulate the annual cycle of the upper-ocean dynamics and its influence on ocean properties in the tropical western Indian Ocean. Surface winds and heat fluxes from the National Centers for Environmental Prediction (NCEP) reanalysis forced the model (Model_NCEP) with initial and lateral boundary conditions derived from the Simple Ocean Data Assimilation (SODA). The model findings were in good agreement with previous research, satellite and observational data as well as another model configuration forced by Comprehensive Ocean and Atmosphere Data Sets (COADS). The initial and lateral boundary conditions for Model_COADS were extracted from World Ocean Atlas 2001. Anticyclonic wind stress curl occurred to the north of Madagascar, and extended towards the Tanzanian coast throughout the year, leading to Ekman convergence and downwelling in that region. The lowest sea-surface height values during the year occurred between 5° and 12° S with an elongated and contracted shape. The East African Coastal Current (EACC) was in phase with the westward North-East Madagascar Current (NEMC) throughout the year with volume transports peaking in June through July in the model forced by NCEP reanalysis. The variability of the volume transport, ocean currents, temperature and salinity to the north of Madagascar on the path of the NEMC mirrored those in the middle Tanzanian shelf on the path of the EACC throughout the year. The NEMC seemed to influence the water masses on the Tanzanian shelf, with cooler and lower-salinity water in the South-West Monsoon, and warmer and saltier water during the North-East Monsoon.

We propose a robust and imperceptible spectral watermarking method for high rate embedding of a watermark into 3D polygonal meshes. Our approach consists of four main steps: (1) the mesh is partitioned into smaller sub-meshes, and then the watermark embedding and extraction algorithms are applied to each sub-mesh, (2) the mesh Laplacian spectral compression is applied to the sub-meshes, (3) the watermark data is distributed over the spectral coefficients of the compressed sub-meshes, (4) the modified spectral coefficients with some other basis functions are used to obtain uncompressed watermarked 3D mesh. The main attractive features of this approach are simplicity, flexibility in data embedding capacity, and fast implementation. Extensive experimental results show the improved performance of the proposed method, and also its robustness against the most common attacks including the geometric transformations, adaptive random noise, mesh smoothing, mesh cropping, and combinations of these attacks.

A Petrov–Galerkin method for computations of fully enclosed flows is developed. It makes use of divergence‐free basis functions which also satisfy the boundary conditions for the velocity field. This allows the elimination of the unknown pressure. The computational procedure reduces to the solution of a system of non‐linear first‐order ordinary differential equations for the spectral expansion coefficients. We illustrate the effectiveness and accuracy of the method by solving the problem of the two‐dimensional thermoconvective flow in a rectangular cavity of aspect ratio 8 at Rayleigh number 3.4×105. Copyright © 2002 John Wiley & Sons, Ltd.

A nitrogen balancing scheme for ocean color data assimilation in general circulation models is described and its potential for improving air-seaCO2 flux estimates is demonstrated. Given increments for phytoplankton, obtainable from a univariate surface chlorophyll analysis, the scheme determines mixed layer concentration increments for the other nitrogen pools: zooplankton, detritus and dissolved inorganic nitrogen (DIN). The fraction of the phytoplankton increment to be balanced by changing DIN varies dynamically with the likely contributions of phytoplankton growth and loss errors to the error in the background state. Further increments are applied below the mixed layer wherever positive DIN increments in shallower layers would otherwise cause the creation of unrealistic sub-surface minima. Total nitrogen at each grid point is conserved where possible. The scheme is evaluated by 1-D twin experiments for two contrasting locations in the North Atlantic, in which synthetic chlorophyll observations are assimilated in an attempt to recover known system trajectories generated by perturbing model parameters. Dissolved inorganic carbon (DIC) and alkalinity tracers, controlled by the nitrogen dynamics, determine the biological modification of sea-water pCO2 at the ocean surface. Assimilation affects DIC and alkalinity directly, the increments being inferred from the nitrogen increments, as well as having a post-analysis effect via the dynamics. It gives major improvements in surface pCO2 at 50N but less improvement at 30N where errors in the phytoplankton nitrogen:chlorophyll ratio cause it to have a detrimental effect in summer. Beneficial effects of nitrogen balancing are demonstrated by comparison with experiments in which only phytoplankton and DIC are updated in the analysis.

SummaryWe present the development and field application of a workflow for multiscale reservoir-model calibration that seamlessly integrates production data into the reservoir description from the facies to the grid-cell scale. To start with, the permeability field is parameterized using a novel grid-connectivity-based transformation basis that can be applied with any model geometry, including unstructured and corner-point grids. The parameterization basis functions emerge from spectral decomposition of the grid-connectivity Laplacian and are related to the structural harmonics of the grid. To reconcile data with model resolution during history matching, we first use the coarsest-scale basis functions to identify the large-scale variability. Additional smaller-scale basis elements are then adaptively incorporated to successively refine the model to a level supported by data resolution. During refinement, the inclusion of more detailed basis functions into the parameterization is determined by generic modal frequency when the prior model is unavailable or by using prior information when available. In the final step of the workflow, a streamline-based inversion is performed to locally adjust the reservoir model at grid-cell resolution along preferential-flow paths defined during the coarser-scale parameterization.We demonstrate the suitability and effectiveness of the developed workflow through application to an offshore turbidite reservoir with frequent well intervention, including shut-ins and recompletions. The static model has over 300,000 cells, a complex channelized interpretation with faults, four injector/producer pairs with deviated wells, and over eight years of production history, including water cut and pressure data. The grid-connectivity-based parameterization effectively updates the prior regional permeability at scales and in locations warranted by the data, while preserving the geologic continuity and avoiding ad hoc redefinition of regions given the sparse well pattern. The multiscale calibrated-permeability field indicates flow communication previously unrecognized in static geologic interpretation or manual history matching.

Among the ways of enhancement of functional capabilities of antenna-feeder devices on the basis of slot coupling elements one is partial filling of the slot cavity by a dielectric medium. Solution of the scattering problem with the use of the continuity condition for the tangential component of the magnetic field on the slot surfaces is reduced to a set of linear algebraic equations of the Galerkin method whose matrix elements represent partial conductions of the slot. In the present paper, analytical expressions have first been derived for partial internal conductions of a longitudinal slot with a layered dielectric filling cut in the wider wall of a rectangular waveguide. The LEq0 eigenmodes of a rectangular waveguide partially filled with a dielectric material are used in the capacity of the basis functions in the Galerkin procedure. Frequency dependences of the intrinsic and transfer conductances of the slot are analyzed. It is shown that by changing the dielectric layer parameters in the slot it is possible to control the active and reactive components of the intrinsic conductivity of the slot which effect can be used for controlling the characteristics of slotted waveguide antenna arrays.

Bubble growth and collapse in viscoelastic liquids analyzed

An alternate approach to the standard harmonic balance method (based on Fourier transforms) is proposed. The proposed method begins with an idea similar to the harmonic balance method, i.e. to transform the initial set of differential equations of the dynamics to a set of discrete algebraic equations. However, as distinct from previous harmonic balance techniques, the proposed method uses a set of basis functions which are localized in time and are not necessarily sinusoidal. Also as distinct from previous harmonic balance methods, the algebraic equations obtained after the transformation of the differential equations of the dynamics are solved in the time domain rather than the frequency domain. Numerical examples are provided to demonstrate the performance of the method for autonomous and forced dynamics of a Van der Pol oscillator.

A mesh-free method with arbitrary-order accuracy for acoustic wave propagation

Abstract

Empirical mode decomposition (EMD) is a favorite tool for analyzing nonlinear and non-stationary signals. It decomposes any signal into a finite set of oscillation modes consisting of intrinsic mode functions and a residual function. Superimposing all these modes reconstructs the signal without any information loss. In addition to satisfying the perfect reconstruction property, however, there is no implication about the reconstruction optimality of the EMD. The lack of optimality restricts the signal recovery capability of the EMD in the presence of disturbances. Only a few attempts are made to meet this deficiency. In this paper, we propose a new algorithm named as time-varying weighted EMD. By this algorithm, original signal is reconstructed in the minimum mean-square error sense through the EMD followed by time-varying weightings of the oscillation modes. Determining the time-varying weights for the oscillation modes constitutes the backbone of the algorithm. Aiming to determine the time-varying weights of the oscillation modes; we use multiple sets of basis functions. The effectiveness of the proposed algorithm is demonstrated by computer simulations involving real biomedical signals. Simulation results show that the proposed algorithm exhibits better performance than that of its existing counterparts in terms of lower mean-square error and higher signal-to-error ratio.

Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocal1 except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series representations of reciprocals of periodic functions. Thus the usual summation techniques employed to evaluate series representations of nonsquare-integrable periodic functions may, in some instances, be circumvented.