Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95

Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.

Spatial tessellations. Concepts and Applications of Voronoi diagrams

[1] The variability of space weather can best be captured using total electron content (TEC), which corresponds to total number of electrons on a ray path. The dual-frequency ground based GPS receivers provide a cost-effective means for monitoring TEC. Computation of TEC for a single GPS station is a challenge due to various unknowns and ambiguities such as inter-frequency receiver bias and satellite bias, choice of mapping function, and peak height of ionosphere for ionospheric piercing point. In this study, IONOLAB group introduces a robust, automatic, online computation routine near-real time TEC, IONOLAB-TEC, for IGS and/or EUREF stations from www.ionolab.org. The user can choose online one station or multiple stations, date or dates for the computation. The IONOLAB-TEC values can be compared with TEC estimates from IGS analysis centers. The output can be obtained either in graphical form, or IONOLAB-TEC estimates can be provided in an excel file. The service is easy to use with a graphical user interface. This unique and original space weather application is provided online, and IONOLAB-TEC estimates are downloaded automatically to the user defined directories under user defined filenames.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/swe.20054

Online, automatic, near‐real time estimation of GPS‐TEC: IONOLAB‐TEC

Uniformly sampled images are often used to interpolate other data acquired more sparsely with an entirely different mode of measurement. For example, downhole tools enable geophysical properties to be measured with high precision near boreholes that are scattered spatially, and less precise seismic images acquired at the earth’s surface are used to interpolate those properties at locations far away from the boreholes. Image-guided interpolation is designed specifically to enhance this process. Most existing methods for interpolation require distances from points where data will be interpolated to nearby points where data are known. Image-guided interpolation requires non-Euclidean distances in metric tensor fields that represent the coherence, orientations and shapes of features in images. This requirement leads to a new method for interpolating scattered data that I call blended neighbor interpolation. For simple Euclidean distances, blended neighbor interpolation resembles the classic natural neighbor interpolation.

/pdf/image-guided-blended-neighbor-interpolation-of-scattered-2f65uugrcv.pdf

Image-guided Blended Neighbor Interpolation of Scattered Data

This work presents a contribution to the understanding of the ionospheric triggering of L-band scintillation in the region over Sao Paulo state in Brazil, under high solar activity. In particular, a climatological analysis of Global Navigation Satellite Systems (GNSS) data acquired in 2012 is presented to highlight the relationship between intensity and variability of the total electron content (TEC) gradients and the occurrence of ionospheric scintillation. The analysis is based on the GNSS data acquired by a dense distribution of receivers and exploits the integration of a dedicated TEC calibration technique into the Ground Based Scintillation Climatology (GBSC), previously developed at the Istituto Nazionale di Geofisica e Vulcanologia. Such integration enables representing the local ionospheric features through climatological maps of calibrated TEC and TEC gradients and of amplitude scintillation occurrence. The disentanglement of the contribution to the TEC variations due to zonal and meridional gradients conveys insight into the relation between the scintillation occurrence and the morphology of the TEC variability. The importance of the information provided by the TEC gradients variability and the role of the meridional TEC gradients in driving scintillation are critically described.

/pdf/l-band-scintillations-and-calibrated-total-electron-content-20sxdrpxfk.pdf

L-band scintillations and calibrated total electron content gradients over Brazil during the last solar maximum

Maps of the total electron content (TEC) of the ionosphere can be reconstructed using data extracted from global positioning system (GPS) signals. For historic and other sparse data sets, the reconstruction of TEC images is often performed using a multivariate interpolation technique. Although there are many interpolation methods available, only a limited number, for example kriging, have been applied to TEC data. This paper presents a quantitative comparison of various commonly used algorithms for scattered-data interpolation over a range of sparsi- ties. Techniques evaluated include a relatively new approach called Adaptive Normalized Convolution (ANC) that has not previously been applied to ionospheric reconstruction. The proposed evaluation scheme employs a quantitative methodology applied to both simulated and real TEC data. Results show that, although the performance of kriging is good in many cases, it is several times worse than the best performing techniques at some sparsities. Natural-neighbor interpolation has a better overall performance than kriging for both simulated and TEC data. Although its performance is a few percent worse than other methods for the simulated data, ANC produces the best performance for the TEC reconstructions.

/pdf/an-evaluation-of-interpolation-techniques-for-reconstructing-n842l64i4m.pdf

An Evaluation of Interpolation Techniques for Reconstructing Ionospheric TEC Maps

Interpolation methods are widely used in geoscience applications to reconstruct multivariate data from irregular samples. This paper describes a quantitative methodology for assessing the performance of various state-of-the-art interpolation methods. The methodology consists of simulation-validation and cross-validation using simulated and real data respectively, and has recently been applied to study the reconstruction of total electron content maps of the ionosphere. These two approaches are described and a study of the various artefacts associated with different interpolation methods also presented, including their origins and typical locations. Finally, the use of the statistical moments of error histograms as a method of evaluating techniques for biases and skew is described, as well as providing confidence bounds on error values. The methodology and artefact analysis should be of use to anyone who uses multivariate interpolation methods.

https://purehost.bath.ac.uk/ws/files/380045/IGARSSJul2008_Foster.pdf

Performance Evaluation of Multivariate Interpolation Methods for Scattered Data in Geoscience Applications

In this letter, a new approach to tracking the ionospheric-storm enhancements known as tongues of ionization (TOIs) is presented. In contrast to conventional model-based methods, the technique works by applying block-based motion estimation methods directly to ionospheric total electron content image sequences. Solutions to the particular problems posed by the low image resolution and the nonrigid motion of the TOIs are proposed. Experimental results for an image sequence covering the 2003 ldquoHalloween stormrdquo establish that the approach produces estimated motion fields that show a good correspondence with the observable motion when the interframe differences are not extreme.

/pdf/tongue-of-ionization-motion-estimation-from-polar-tec-dptqjz6m5x.pdf

M.P. Foster

Papers

An Evaluation of Interpolation Techniques for Reconstructing Ionospheric TEC Maps

Performance Evaluation of Multivariate Interpolation Methods for Scattered Data in Geoscience Applications

Tongue of Ionization Motion Estimation From Polar TEC Sequences