GNGTS 2022 - Atti del 40° Convegno Nazionale

504 GNGTS 2022 Sessione 3.3 INTRODUCTION TO INTERPOLATION UNCERTAINTY OF THE NATURAL NEIGHBORS METHOD (SIBSON) M. Iurcev 1 , M. Majostorovic 2 , F. Pettenati 1 1 Istituto di Oceanografia e di Geofisica Sperimentale, OGS, Trieste, Italy 2 Università degli studi di Trieste, Trieste, Italy Introduction. The Natural Neighbors (Sibson 1980) (NN hereafter) method is a spatial data interpolation method with unique reproducibility (Iurcev et al., 2021). What this method lacks is a qualitative and/or quantitative control of the uncertainty based on the random spatial distribution of the measurements, relative to the true surface of the data. The method is an exact interpolator, in the sense that the original data values are preserved at reference data points. A method such as Kriging, which is considered the BLUE (Best Linear Unbiased Estimator) (Chilès and Delfiner, 1999) inherently provides an assessment of errors, through the minimization of the mean square error. However, Kriging requires several input parameters, a trend analysis for the stationary condition and as main ingredient a semivariogram model in order to estimate the weights which minimize the error variance (for the Universal Kriging version). One approach to assess the uncertainties in NN is based on cross-validation errors Etherington (2020). This approach involves the computation of the Mean Absolute Error (cross-validation) of the estimate value f * over data f i , taking into account the mutual distances between these points. In this note we follow a geostatistical approach that addresses the variance and the spatial structure of the data with respect to the interpolation points. Method. Let us consider N points in ℝ 2 , with coordinates x i (i=1…N). We generate a partition of the plane by means of a Voronoi tessellation. The V i convex polygons have the following property (1) and the tessellation is uniquely determined (Fig. 1). Fig. 1 - Voronoi tessellation of a spatial random distribution of x i data.