Center Of Grid Cell Research Articles

Thalweg and Ridge Network Extraction From Unaltered Topographic Data as a Basis for Terrain Partitioning

AbstractHigh‐resolution grid digital elevation models (DEMs) are increasingly used by scientists and engineers to describe the current state and evolution of Earth and planetary topography. These data, however, are commonly altered by depression filling and grid coarsening procedures. Alteration of observed topographic data may cause significant information loss and limit the capabilities of models. This study shows that physically meaningful thalweg and ridge networks can be extracted automatically from any unaltered high‐resolution grid DEM, and that these networks can be used as bases for terrain partitioning. The slopeline network connecting grid cell centers is used to identify ridge points as those grid cell border midpoints and vertices that are not crossed by slopelines. From each ridge point, the average length of the two slopelines extending on the opposite slopes of the ridge until they rejoin is then computed. Based on these lengths, exorheic and endorheic basins are identified. Thalwegs of exorheic and endorheic basins are finally connected through spilling saddles to form the thalweg network. The related ridge network is identified based on neighboring relationships between ridge points. Thalweg and ridge networks are hierarchized using the well‐known concept of drainage area and an extended concept of dispersal area to inform terrain partitioning at any level of detail. Observed topographic features are well reproduced by extracted networks. The impact of preserving depressions over mountain areas is evaluated, and the benefits from unstructured terrain partitioning based on thalweg and ridge networks in the description of flood plain inundation are illustrated.

Improved Incompressible Material Point Method Based on Particle Density Correction

In the incompressible material point method (iMPM), the momentum equations were solved at the background grid nodes while the divergence-free conditions were enforced at grid cell centers. The density of each particle was assumed to be constant but the particles could distribute nonuniformly in space over time. Therefore, the fluid density would be nonuniform and violate the incompressible condition. In this paper, the original iMPM is improved by explicitly imposing the density-invariant condition. A new particle shifting scheme is proposed for particle density correction. Particles are shifted along their density gradient to guarantee that the density field of the fluid is constant and the momentum is conserved. The proposed method has been implemented in our MPM code, and validated by simulating a dam breaking inside a tank, another dam breaking with an obstacle and a sloshing problem.

Hydrography‐Driven Coarsening of Grid Digital Elevation Models

AbstractA new grid coarsening strategy, denoted as hydrography‐driven coarsening, is developed in the present study. The hydrography‐driven coarsening is designed to retain the essential hydrographic features of valleys and channels observed in high‐resolution digital elevation models: (1) depressions are filled in the considered high‐resolution digital elevation model, (2) the obtained topographic data are used to extract a reference grid network composed of all surface flow paths, (3) the Horton order is assigned to each link of the reference grid network, and (4) within each coarse grid cell, the elevation of the point lying along the highest‐order path of the reference grid network and displaying the minimum distance to the cell center is assigned to this coarse grid cell center. The capabilities of the hydrography‐driven coarsening to provide consistent surface flow paths with respect to those observed in high‐resolution digital elevation models are evaluated over a synthetic valley and two real drainage basins located in the Italian Alps and in the Italian Apennines. The hydrography‐driven coarsening is found to yield significantly more accurate valley and channel profiles than existing coarsening strategies. In absolute terms, the obtained valleys and channels compare favorably with those observed. In addition, the proposed coarsening strategy is found to reduce drastically the impact of depression‐filling in the obtained coarse digital elevation models. The hydrography‐driven coarsening strategy is therefore advocated for all those cases in which the relief of the extracted drainage network is an important hydrographic feature.

Off-Grid Radar Coincidence Imaging Based on Variational Sparse Bayesian Learning

Radar coincidence imaging (RCI) is a high-resolution staring imaging technique motivated by classical optical coincidence imaging. In RCI, sparse reconstruction methods are commonly used to achieve better imaging result, while the performance guarantee is based on the general assumption that the scatterers are located at the prediscretized grid-cell centers. However, the widely existing off-grid problem degrades the RCI performance considerably. In this paper, an algorithm based on variational sparse Bayesian learning (VSBL) is developed to solve the off-grid RCI. Applying Taylor expansion, the unknown true dictionary is approximated accurately to a linear model. Then target reconstruction is reformulated as a joint sparse recovery problem that recovers three groups of sparse coefficients over three known dictionaries with the constraint of the common support shared by the groups. VSBL is then applied to solve the problem by assigning appropriate priors to the three groups of coefficients. Results of numerical experiments demonstrate that the algorithm can achieve outstanding reconstruction performance and yield superior performance both in suppressing noise and in adapting to off-grid error.

Radar Coincidence Imaging for Off-Grid Target Using Frequency-Hopping Waveforms

Radar coincidence imaging (RCI) is a high-resolution staring imaging technique without the limitation of the target relative motion. To achieve better imaging performance, sparse reconstruction is commonly used. While its performance is based on the assumption that the scatterers are located at the prediscretized grid-cell centers, otherwise, off-grid emerges and the performance of RCI degrades significantly. In this paper, RCI using frequency-hopping (FH) waveforms is considered. The off-grid effects are analyzed, and the corresponding constrained Cramér-Rao bound (CCRB) is derived based on the mean square error (MSE) of the “oracle” estimator. For off-grid RCI, the process is composed of two stages: grid matching and off-grid error (OGE) calibration, where two-dimension (2D) band-excluded locally optimized orthogonal matching pursuit (BLOOMP) and alternating iteration minimization (AIM) algorithms are proposed, respectively. Unlike traditional sparse recovery methods, BLOOMP realizes the recovery in the refinement grids by overwhelming the shortages of coherent dictionary and is robust to noise and OGE. AIM calibration algorithm adaptively adjusts the OGE and, meanwhile, seeks the optimal target reconstruction result.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

Non-hydrostatic modeling of wave interactions with porous structures

This paper presents a three-dimensional non-hydrostatic wave model NHWAVE for simulating wave interactions with porous structures. The model calculates the porous media flow based on well-balanced volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS) in σ coordinate. The turbulence field within the porous structures is simulated by an improved k−ϵ model. To account for the temporally varying porosity at the grid cell center introduced by the variation of free surface elevation, the porosity is updated at each time step in the computation. The model is calibrated and validated using a wide range of laboratory measurements, involving dam-break flow through porous media, 3D solitary wave interactions with a porous structure, 2D solitary wave interactions with a submerged permeable obstacle as well as periodic wave breaking over a submerged porous breakwater with steep slopes. The model is shown to be capable of well simulating wave reflection, diffraction, wave breaking and wave transmission through porous structures, as well as the turbulent flow field around the permeable structures. It is also demonstrated in the paper that the current non-hydrostatic model is computationally much more efficient than the existing porous flow models based on VOF approach. The non-hydrostatic wave model NHWAVE can be a useful tool for studying wave–structure interactions.

Estimates of surface normal and curvature, reconstruction of continuum surface force model, and elimination of spurious currents

SUMMARYA reconstructed continuum surface force (CSF) model is presented for the volume‐of‐fluid (VOF) method in numerical simulations of surface tension‐driven flow. The gradient of VOF function yielded by the one‐direction difference (ODD) algorithm has second‐order accuracy in one direction and exhibits unit pulse function in the other direction. Use of our ODD algorithm for surface normal and curvature improves the accuracy of surface tension force estimate and meets the necessary condition of a circular droplet free of spurious currents. The immersed length, a physical depth of grid cell center introduced in this paper, is computed from VOF function and surface orientation. It is chosen instead of VOF function as weight parameters in the evaluations of density and volumetric surface tension force between interfacial grid cells. Grid cells and control cells are classified into interfacial, sublayer, and interior cells according to their distances to interface. Surface tension is thus constructed within interfacial or sublayer cells. The numerical approach is modified so that flow pressure solutions are sought only at those immersed grid cell centers. The transitional region from one fluid to the other is compressed. Spurious currents by no means grow on free surface in the numerical simulations using our algorithms and reconstructed CSF model. The simulation results agree with the Laplace pressure jump across a static circular free surface or experimental observations. Copyright © 2014 John Wiley & Sons, Ltd.

A Hybrid Staggered/Semistaggered Finite-Difference Algorithm for Solving Time-Dependent Incompressible Navier-Stokes Equations on Curvilinear Grids

An accurate and efficient finite-difference method for solving the incompressible Navier-Stokes equations on curvilinear grids is developed. This method combines the favorable features of the staggered grid and semistaggered grid approaches. All components of velocity are stored at the corner vertices, and pressure is stored at the grid cell centers. All components of the momentum equations are discretized at cell vertices, facilitating a consistent discretization of the diffusive and convective terms as the boundaries are approached. The Christoffel symbol does not appear in the transformed equations and the cost of computation is comparable to that of the staggered-grid approach. A projection method is used to effectively evolve the discrete system in time, while ensuring a divergence-free velocity field. The discrete divergence and gradient operators of the projection step are constructed on a staggered gird layout leading to exact satisfaction of the discrete continuity. The solution of the Poisson-Neumann equation in the projection step is free of any spurious eigenmodes. The validity of the method is demonstrated on four benchmark problems. The Taylor-Green vortex problem is solved on a curvilinear grid with highly skewed cells and a second-order convergence in l ∞-norm is observed. The mixed convection in a lid-driven cavity is solved on a highly curvilinear grid and excellent agreement with literature is obtained. The results for flow past a cylinder and pusatile flow in a 90° bend are compared with the existing experimental data in the literature. The predictions agree well with the measured data, and validate the approach used.

M3G: maximum margin microarray gridding.

BackgroundComplementary DNA (cDNA) microarrays are a well established technology for studying gene expression. A microarray image is obtained by laser scanning a hybridized cDNA microarray, which consists of thousands of spots representing chains of cDNA sequences, arranged in a two-dimensional array. The separation of the spots into distinct cells is widely known as microarray image gridding.MethodsIn this paper we propose M3G, a novel method for automatic gridding of cDNA microarray images based on the maximization of the margin between the rows and the columns of the spots. Initially the microarray image rotation is estimated and then a pre-processing algorithm is applied for a rough spot detection. In order to diminish the effect of artefacts, only a subset of the detected spots is selected by matching the distribution of the spot sizes to the normal distribution. Then, a set of grid lines is placed on the image in order to separate each pair of consecutive rows and columns of the selected spots. The optimal positioning of the lines is determined by maximizing the margin between these rows and columns by using a maximum margin linear classifier, effectively facilitating the localization of the spots.ResultsThe experimental evaluation was based on a reference set of microarray images containing more than two million spots in total. The results show that M3G outperforms state of the art methods, demonstrating robustness in the presence of noise and artefacts. More than 98% of the spots reside completely inside their respective grid cells, whereas the mean distance between the spot center and the grid cell center is 1.2 pixels.ConclusionsThe proposed method performs highly accurate gridding in the presence of noise and artefacts, while taking into account the input image rotation. Thus, it provides the potential of achieving perfect gridding for the vast majority of the spots.

Determination of surface flow paths from gridded elevation data

Surface flow paths are obtained from gridded elevation data by connecting grid cell centers along predetermined flow directions. These flow directions are commonly determined using single and multiple flow direction algorithms. It remains, however, unclear whether multiple flow direction algorithms, which introduce artificial dispersion, can be used to describe surface flow paths and gravity‐driven processes across a terrain without causing unrealistic flow dispersion. To explore this issue, a unified algorithm for the determination of flow directions has been developed, and new methods for the validation of the resulting surface flow paths are introduced. The unified algorithm makes it possible, by setting appropriate parameters, to perform local or path‐based analyses and to experiment with different combinations of single and multiple flow directions in a morphologically significant manner. The new validation methods use drainage systems delineated from contour elevation data as a reference and take into consideration the overlap between these systems and those obtained from gridded elevation data. The unified algorithm is presented, and the results are evaluated for selected case studies in order to provide guidance on the use of surface flow path algorithms based on gridded elevation data.

2-DAL SIMULATION OF EM FIELDS RADIATED BY ROTATING CYLINDER CARRYING SURFACE CURRENTS USING PASSING CENTER SWING BACK GRIDS TECHNIQUE

The passing center swing back grids (PCSBG) technique, in conjunction with the method of characteristics (MOC), was proposed to model electromagnetic problems featured with rotating objects. The drive of this proposal lays mainly on the fact that MOC deflnes all fleld components in the center of grid cell. Its practicability was validated by exhibiting the radiated EM flelds from a rotating cylinder which carries surface currents with Gaussian proflle and ∞owing in the axial direction. To clearly demonstrate that the cylinder is rotating and radiating EM flelds simultaneously, the following arrangements were made. The cylinder may be equally sliced into an even number of segments that are with and without currents alternatively since a rotating circular cylinder yields no relativistic efiects. The computational results showed that the radiated electromagnetic flelds bear vortex structures as the cause of rotating cylinder, which serves as the evidences that PCSBG works properly.

Numerically Solving Scattered Electromagnetic Fields from Rotating Objects Using Passing Center Swing Back Grids Technique: A Proposal

In this paper the author proposes an idea and explains the feasibility of the useful approach to help to model electromagnetic scattering problems featured with rotating objects. This technique, passing center swing back grids (PCSBG), in conjunction with the method of characteristics (MOC), is devised especially for the numerical solution of the time-domain Maxwell's equations where the electromagnetic fields are scattered from rotating objects. On solving such type of problems, one noticeable advantage of MOC over other computational electromagnetics approaches is that MOC defines all field components in the center of grid cell, on which the PCSBG technique is based and reasoned to be feasible.

Spatial Statistics in the Presence of Location Error with an Application to Remote Sensing of the Environment

Techniques for the analysis of spatial data have, to date, tended to ignore any effect caused by error in specifying the spatial locations at which measurements are recorded. This paper reviews the methods for adjusting spatial inference in the presence of data-location error, particularly for data that have a continuous spatial index (geostatistical data). New kriging equations are developed and evaluated based on a simulation experiment. They are also applied to remote-sensing data from the Total Ozone Mapping Spectrometer instrument on the Nimbus-7 satellite, where the location error is caused by assignment of the data to their nearest grid-cell centers. The remote-sensing data measure total column ozone (TCO), which is important for protecting the Earth's surface from ultraviolet and other radiation.