Interpolation of spatial data – A stochastic or a deterministic problem?

Scheuerer, Michael; Schaback, Robert; Schlather, Martin

doi:10.1017/s0956792513000016

Cited by 85 publications

(76 citation statements)

References 81 publications

(106 reference statements)

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“…Our particular choice is a compromise between flexibility-even for average temperatures we sometimes observe inversions and our model should be able to deal with them-and availability of a sufficient amount of data at high altitudes. The corresponding kriging system is solvable if the three B-spline basis functions, considered as functions in s, and the horizontal co-ordinates are linearly independent on the set S obs (for mathematical details see also Scheuerer et al (2013)).…”

Section: Spatial Interpolation Ofȳ S and ξ 2 Smentioning

confidence: 99%

Spatially Adaptive Post-Processing of Ensemble Forecasts for Temperature

Scheuerer

Büermann

2013

Journal of the Royal Statistical Society Series C: Applied Statistics

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We propose an extension of the non-homogeneous Gaussian regression (NGR) model by Gneiting et al. (2005) that yields locally calibrated probabilistic forecasts of tem- perature, based on the output of an ensemble prediction system (EPS). Our method represents the mean of the predictive distributions as a sum of short-term averages of local temperatures and EPS-driven terms. For the spatial interpolation of temperature averages and local forecast uncertainty parameters we use a Gaussian random field model with an intrinsically stationary component that captures large scale fluctuations and a location-dependent nugget effect that accounts for small scale variability. Based on the dynamical forecasts by the COSMO-DE-EPS and observational data over Germany we evaluate the performance of our method and and compare it with other post-processing approaches such as geostatistical model averaging. Our method yields locally calibrated and sharp probabilistic forecasts and compares favorably with other approaches. It is reasonably simple, computationally efficient, and therefore suitable for operational usage in the post-processing of temperature ensemble forecasts

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Section: Spatial Interpolation Ofȳ S and ξ 2 Smentioning

confidence: 99%

Spatially Adaptive Post-Processing of Ensemble Forecasts for Temperature

Scheuerer

Büermann

2013

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…The interpolation of 0-increments provides an effective method of handling multilevel data (representing the contacts between multiple stratigraphic horizons) where no unconformities or discontinuities exist. Thorough comparative analyses of RBF and kriging interpolation methods can be found in Matheron (1981), Dubrule (1984), Myers (1992) and Scheuerer et al (2013). We believe that both approaches can mutually benefit from the vast amount of research completed on each.…”

Section: Mathematical Frameworkmentioning

confidence: 99%

“…1 + (εr ) 2 ) are well known for modelling topography and other irregular open surfaces (Hardy 1971(Hardy , 1990. It is important to note that numerical techniques, such as leave one out cross validation (LOOCV), are available to optimally choose the best RBF and, if applicable, the shape parameter ε, using a particular dataset (Fasshauer 2007b;Scheuerer et al 2013). …”

Section: Radial Basis Function Selectionmentioning

confidence: 99%

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

et al. 2014

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A generalized interpolation framework using radial basis functions (RBF) is presented that implicitly models three-dimensional continuous geological surfaces from scattered multivariate structural data. Generalized interpolants can use multiple types of independent geological constraints by deriving for each, linearly independent functionals. This framework does not suffer from the limitations of previous RBF approaches developed for geological surface modelling that requires additional offset points to ensure uniqueness of the interpolant. A particularly useful application of generalized interpolants is that they allow augmenting on-contact constraints with gradient constraints as defined by strike-dip data with assigned polarity. This interpolation problem yields a linear system that is analogous in form to the previously developed potential field implicit interpolation method based on co-kriging of contact increments using parametric isotropic covariance functions. The general form of the mathematical framework presented herein allows us to further expand on solutions by: (1) including stratigraphic data from above and below the target surface as inequality constraints (2) modelling anisotropy by data-driven eigen analysis of gradient constraints and (3) incorporating additional constraints by adding linear functionals to the system, such as fold axis constraints. Case studies are presented that demonstrate the advantages and general performance of the surface modelling method in sparse data environments where the contacts that constrain geological surfaces are rarely exposed but structural and off-contact stratigraphic data can be plentiful. Electronic supplementary materialThe online version of this article (

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“…RKHS interpolation is known to be (see [21]) equivalent to interpolation by Kriging, also known as Gaussian process metamodelling. Using n evaluations of f , one can build a training sample consisting of n input-output pairs D = {(x 1 , y 1 ), .…”

Section: Rkhs Interpolation and Error Boundmentioning

confidence: 99%