Global-Krigger: A Global Kriging Interpolation Toolbox With Paleoclimatology Examples

Abstract

Many applications in Earth sciences require spatial prediction, that is, obtaining a continuous scalar field from a set of discrete scalar data points on the Earth's surface. Such applications include model-data comparisons and derivation of continuous scalar fields as input for Earth system models. The advantage of kriging as an interpolation method is that it provides predictions with confidence intervals for data sets of irregularly distributed points in space. However, the theory of kriging for non-Euclidean domains such as oblate spheroids (e.g., the Earth's surface) is poorly developed, and existing kriging algorithms for global interpolation oftentimes cannot guarantee the validity of their predictions. Here, we present Global-Krigger, a new kriging interpolation algorithm adapted for local to global applications that (a) incorporates a numerical check to guarantee that the necessary conditions for the kriging system of linear equations are met, and (b) derives a combined uncertainty field due both to spatial variations in data density and measurement error. The robustness of the method is demonstrated by cross-validating predictions against reanalysis fields of traditional climatological scalar variables. We also show an example application in paleoclimatology for Holocene mineral dust deposition fluxes. The toolbox includes a user-friendly graphical user interface that guides users through a range of choices during data pre-interpolation analysis, kriging, and post-processing.