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A Comparison of Interpolation Methods for Sparse Data: Application to Wind and Concentration Fields
In order to produce gridded fields of pollutant concentration data and surface wind data for use in an air quality model, a number of techniques for interpolating sparse data values are compared. The techniques are compared using three data sets. One is an idealized concentration distribution to which the exact solution is known, the second is a potential flow field, while the third consists of surface ozone concentrations measured in the Los Angeles Basin on a particular day. The results of the study indicate that fitting a second-degree polynomial to each subregion (triangle) in the plane with each data point weighted according to its distance from the subregion provides a good compromise between accuracy and computational cost
Interpolation and scattered data fitting on manifolds using projected PowellāSabin splines
We present methods for either interpolating data or for fitting scattered data on a two-dimensional smooth manifold. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of a family of charts {(UĪ¾ , Ī¾)}Ī¾ā satisfying certain conditions of smooth dependence on Ī¾. If is a C2-manifold embedded into R3, then projections into tangent planes can be employed. The data fitting method is a two-stage method. We prove that the resulting function on the manifold is continuously differentiable, and establish error bounds for both methods for the case when the data are generated by a smooth function
Evaluating the Differences of Gridding Techniques for Digital Elevation Models Generation and Their Influence on the Modeling of Stony Debris Flows Routing: A Case Study From Rovina di Cancia Basin (North-Eastern Italian Alps)
Debris \ufb02ows are among the most hazardous phenomena in mountain areas. To cope
with debris \ufb02ow hazard, it is common to delineate the risk-prone areas through
routing models. The most important input to debris \ufb02ow routing models are the
topographic data, usually in the form of Digital Elevation Models (DEMs). The quality
of DEMs depends on the accuracy, density, and spatial distribution of the sampled
points; on the characteristics of the surface; and on the applied gridding methodology.
Therefore, the choice of the interpolation method affects the realistic representation
of the channel and fan morphology, and thus potentially the debris \ufb02ow routing
modeling outcomes. In this paper, we initially investigate the performance of common
interpolation methods (i.e., linear triangulation, natural neighbor, nearest neighbor,
Inverse Distance to a Power, ANUDEM, Radial Basis Functions, and ordinary kriging)
in building DEMs with the complex topography of a debris \ufb02ow channel located
in the Venetian Dolomites (North-eastern Italian Alps), by using small footprint full-
waveform Light Detection And Ranging (LiDAR) data. The investigation is carried
out through a combination of statistical analysis of vertical accuracy, algorithm
robustness, and spatial clustering of vertical errors, and multi-criteria shape reliability
assessment. After that, we examine the in\ufb02uence of the tested interpolation algorithms
on the performance of a Geographic Information System (GIS)-based cell model for
simulating stony debris \ufb02ows routing. In detail, we investigate both the correlation
between the DEMs heights uncertainty resulting from the gridding procedure and
that on the corresponding simulated erosion/deposition depths, both the effect of
interpolation algorithms on simulated areas, erosion and deposition volumes, solid-liquid
discharges, and channel morphology after the event. The comparison among the tested
interpolation methods highlights that the ANUDEM and ordinary kriging algorithms
are not suitable for building DEMs with complex topography. Conversely, the linear
triangulation, the natural neighbor algorithm, and the thin-plate spline plus tension and completely regularized spline functions ensure the best trade-off among accuracy
and shape reliability. Anyway, the evaluation of the effects of gridding techniques on
debris \ufb02ow routing modeling reveals that the choice of the interpolation algorithm does
not signi\ufb01cantly affect the model outcomes
An investigation of methods of surface estimation with application to the interpolation of antenna patterns
The problem of estimating a surface from a set of discrete measurements lying along straight lines is considered. This situation arises when one attempts to determine the S-Band antenna gain pattern for the Space Shuttle, from measurements taken at several ground stations. The results of previous investigators concerned with the performance of surface approximation techniques for the present application, are extended in this study by examining the case where the data samples are corrupted by measurement noise. Results have been obtained using least-squares approximation with bicubic B-spline basis functions, and for an interpolation algorithm in conjunction with a spatial smoothing filter. Because of the nature of the data acquisition and the impracticality of the least-squares algorithm when many sample points are used, the application of the Kalman filter to the surface estimation problem is discussed, although no numerical results were obtained using this approach. It is shown that a direct application of Kalman filter theory yields a filter algorithm which would be extremely difficult to implement. Based on the applications of reduced-order, suboptimal filters to image processing, a suboptimal approximation to the Kalman filter, applied to the surface estimation problem, is considered. The use of a decentralized estimation approach to this problem is briefly examined --Abstract, page ii
Contours and Contouring in Hydrography Part II - Interpolation
In Part I of this series, the authors discussed those issues which we feel are fundamentally important and which must be addressed by any method which aims to mechanize the drawing of depth contours for hydrographic charts. In this article we begin the discussion of the How of contouring. In particular, we concentrate on some of the most common methods used in the interpolation of the synthetic surface upon which computed contours will lie
Hybrid Functional-Neural Approach for Surface Reconstruction
ABSTRACT. This paper introduces a new hybrid functional-neural approach for surface reconstruction. Our approach is based on the combination of two powerful artificial intelligence paradigms: on one hand, we apply the popular Kohonen neural network to address the data parameterization problem. On the other hand, we introduce a new functional network, called NURBS functional network, whose topology is aimed at reproducing faithfully the functional structure of the NURBS surfaces. These neural and functional networks are applied in an iterative fashion for further surface refinement. The hybridization of these two networks provides us with a powerful computational approach to obtain a NURBS fitting surface to a set of irregularly sampled noisy data points within a prescribed error threshold. The method has been applied to two illustrative examples. The experimental results confirm the good performance of our approach.This research has been kindly supported by the Computer
Science National Program of the Spanish Ministry of Economy
and Competitiveness, Project ref. no. TIN2012-30768,
Toho University (Funabashi, Japan), and the University of
Cantabria (Santander, Spain)
Adaptive meshless centres and RBF stencils for Poisson equation
We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the mesh-based adaptive finite element method
Temporal and Spatial Variations in Chesapeake Bay Water Quality: A Video Data Report
Over the past two years we have been developing computer programs to investigate various scientific visualization techniques as applied to estuarine data. The original impetus was to be able to visualize the results of the three-dimensional hydrodynamic model under development at the Virginia Institute of Marine Science, College of William and Mary (VIMS). We quickly recognized the superior ability of certain graphic approaches, especially pseudocolor animation, to efficiently transmit a tremendous amount of information to the viewer, allowing the scientist to gain an insight into the dynamics of the data not otherwise available. We decided to apply this technique to the U.S. Environmental Protection Agency (EPA) Bay Monitoring data set, a field collection effort so large that it sometimes overwhelms our traditional information presentations. What we present here is an alternative way of presenting and archiving large amounts of field measurements. The Chesapeake Bay Program began its water quality monitoring in the summer of 1984. Data collection in the mainstem of the Bay was done by University of Maryland (UMD), VIMS, and Old Dominion University (ODU), supported by EPA, while state regulatory agencies have been responsible for water quality data from the Maryland and Virginia tributaries. More than 130 stations ( 49 in the Bay proper) were occupied over 120 times each during the water years 1985 through 1990 (Figure 1). This information has been brought together to create color contoured images of the 10 different physical and water quality parameters that were measured. Each parameter for each month is summarized in a color image that shows the map-view surface and bottom distributions plus a vertical North-South section running down the natural channel from the Susquehanna to the mouth of the Bay, Each pixel in the map-view represents a lkm X lkm area. Although a certain amount of data manipulation must occur between the original logged measurements and these images, the distributions shown should best be understood as raw snapshots of what was present in the Chesapeake during that month. No data analysis or interpretation is attempted in this report
Software for C1 interpolation
The problem of mathematically defining a smooth surface, passing through a finite set of given points is studied. Literature relating to the problem is briefly reviewed. An algorithm is described that first constructs a triangular grid in the (x,y) domain, and first partial derivatives at the modal points are estimated. Interpolation in the triangular cells using a method that gives C sup.1 continuity overall is examined. Performance of software implementing the algorithm is discussed. Theoretical results are presented that provide valuable guidance in the development of algorithms for constructing triangular grids
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