Examination of geostatistical and machine-learning techniques as interpolators in anisotropic atmospheric environments

Selecting which interpolation method to use significantly affects the results of atmospheric studies. The goal of this study is to examine the performance of several interpolation techniques under typical atmospheric conditions. Several types of kriging and artificial neural networks used as spatial interpolators are here compared and evaluated against ordinary kriging, using real airborne CO2 mixing-ratio data and synthetic data. The real data were measured (on December 26, 2012) between Billings and Lamont, near Oklahoma City, Oklahoma, within and above the planetary boundary layer (PBL). Predictions were made all along the flight trajectory within a total volume of 5000 km3 of atmospheric air (27 × 33 × 5.6 km). We evaluated (a) universal kriging, (b) ensemble neural networks, (c) universal kriging with ensemble neural network outputs used as covariates, and (d) ensemble neural networks with ordinary kriging of the residuals as interpolation tools. We found that in certain cases, when the weaknesses of ordinary kriging interpolation schemes (based on an omnidirectional isotropic variogram presumption) became apparent, more sophisticated interpolation methods were in order. In this study, preservation of the potentially nonlinear relationship between the trend and coordinates (by using neural kriging output as a covariate in a universal kriging scheme) was attempted, with varying degrees of success (it was best performer in 4 out of 8 cases). The study confirmed the necessity of selecting an interpolation approach that includes a combination of expert understanding and appropriate interpolation tools. The error analysis showed that uncertainty representations generated by the kriging methods are superior to neural networks, but that the actual error varies from case to case.