Spatial Interpolation contribution to noise maps uncertainty

Noise maps results are usually presented as contour graphs or isophone curves, which describe the sound levels as functions of spatial location. These maps are added to Geographic Information Systems (GIS), allowing sound level evaluation as a function of the continuous coordinates x and y, for a given height above ground. Although the outcome of the system is a continuous variable, the calculations that allow its evaluation are obtained in discrete points that form a calculation grid, which is created by the application of spatial sampling techniques. Using spatial interpolation tools, values are assigned to the locations in which measures or calculations have not been performed. The application of sampling and interpolation techniques (the type of grid, its density, the interpolation algorithms…) contributes to the uncertainty of the results. This paper describes a calculation method to quantify the uncertainty associated to the spatial sampling and interpolation process. We also propose a revision of the classical meaning of noise mapping uncertainty, taking into account the final application of the results

Spatial interpolation of high-frequency monitoring data

Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high density grid, which can then be used to generate meteorological maps at a broad range of spatial and temporal scales. In addition to point predictions, quantifications of uncertainty are also needed. One way to accomplish this is to provide multiple simulations of the relevant meteorological quantities conditional on the observed data taking into account the various uncertainties in predicting a space-time process at locations with no monitoring data. Using a high-quality dataset of minute-by-minute measurements of atmospheric pressure in north-central Oklahoma, this work describes a statistical approach to carrying out these conditional simulations. Based on observations at 11 stations, conditional simulations were produced at two other sites with monitoring stations. The resulting point predictions are very accurate and the multiple simulations produce well-calibrated prediction uncertainties for temporal changes in atmospheric pressure but are substantially overconservative for the uncertainties in the predictions of (undifferenced) pressure.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS208 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Enhanced spatial error concealment with directional entropy based interpolation switching

This paper describes a spatial error concealment method that uses edge related information for concealing missing macroblocks in a way that not only preserves existing edges but also avoids introducing new strong ones. The method relies on a novel switching algorithm which uses the directional entropy of neighboring edges for choosing between two interpolation methods, a directional along detected edges or a bilinear using the nearest neighboring pixels. Results show that the performance of the proposed method is subjectively and objectively (PSNR wise) better compared to both 'single interpolation' and to edge strength based switching methods.This paper describes a spatial error concealment method that uses edge related information for concealing missing macroblocks in a way that not only preserves existing edges but also avoids introducing new strong ones. The method relies on a novel switching algorithm which uses the directional entropy of neighboring edges for choosing between two interpolation methods, a directional along detected edges or a bilinear using the nearest neighboring pixels. Results show that the performance of the proposed method is subjectively and objectively (PSNR wise) better compared to both 'single interpolation' and to edge strength based switching method

Distance in spatial interpolation of daily rain gauge data

Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. The spatial density of available data sites is often changing with time. This paper investigates the application of statistical distance, like one minus common variance of time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation observed in Austria. Choosing statistical distance instead of geographical distance in interpolation of an actually available coarse observation network yields more robust interpolation results at sites of a denser network with actually lacking observations. The performance enhancement is in or close to mountainous terrain. This has the potential to parsimoniously densify the currently available observation network. Additionally, the success further motivates search for conceptual rain-orography interaction models as components of spatial rain interpolation algorithms in mountainous terrain

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing

An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method

An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D

An Ensemble Approach to Space-Time Interpolation

There has been much excitement and activity in recent years related to the relatively sudden availability of earth-related data and the computational capabilities to visualize and analyze these data. Despite the increased ability to collect and store large volumes of data, few individual data sets exist that provide both the requisite spatial and temporal observational frequency for many urban and/or regional-scale applications. The motivating view of this paper, however, is that the relative temporal richness of one data set can be leveraged with the relative spatial richness of another to fill in the gaps. We also note that any single interpolation technique has advantages and disadvantages. Particularly when focusing on the spatial or on the temporal dimension, this means that different techniques are more appropriate than others for specific types of data. We therefore propose a space- time interpolation approach whereby two interpolation methods – one for the temporal and one for the spatial dimension – are used in tandem in order to maximize the quality of the result. We call our ensemble approach the Space-Time Interpolation Environment (STIE). The primary steps within this environment include a spatial interpolator, a time-step processor, and a calibration step that enforces phenomenon-related behavioral constraints. The specific interpolation techniques used within the STIE can be chosen on the basis of suitability for the data and application at hand. In the current paper, we describe STIE conceptually including the structure of the data inputs and output, details of the primary steps (the STIE processors), and the mechanism for coordinating the data and the processors. We then describe a case study focusing on urban land cover in Phoenix, Arizona. Our empirical results show that STIE was effective as a space-time interpolator for urban land cover with an accuracy of 85.2% and furthermore that it was more effective than a single technique.