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

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.Plain Language Summary Many climatic variables such as temperature and precipitation are measured by monitoring stations on the Earth's surface at irregularly distributed locations. Similarly, paleoclimatic proxy variables are available at specific locations where paleoclimatic archives such as marine sediment cores have been retrieved. Such data sets can be used to guide Earth system simulations, but this works best when they are available as a regular grid. Kriging is an interpolation method that produces regular grids from irregularly distributed measurements. However, while kriging theory is well-developed for measurements on a plane surface, its application on curved surfaces is problematic. To improve this, we have developed Global-Krigger, a user-friendly kriging interpolation toolbox for the surface of the Earth. It incorporates new tests to check the validity of kriging results on curved surfaces. The toolbox also provides a quantification of the interpolation uncertainty, taking into account both the uncertainty of the measurements and the spatial distribution of the measurement sites. We show that our algorithm gives robust results by applying it to a sub-sample of known modern climatology fields, and also provides a paleoclimatic application for Holocene mineral dust deposition fluxes. Finally, we develop a graphical user interface to guide users in the process of kriging.

Automated summary

Many Earth science applications require spatial prediction from a set of discrete scalar data points on the Earth's surface. However, kriging theory for non-Euclidean domains like the Earth's surface is not well-developed, and existing global kriging algorithms often cannot guarantee the validity of their predictions. In this study, we present Global-Krigger, a new kriging interpolation algorithm that incorporates a numerical check to ensure the validity of the kriging system and derives an uncertainty field. The algorithm's robustness is demonstrated through cross-validation and an example application in paleoclimatology.