A crossvalidation-based comparison of kriging and IDW in local GNSS/levelling quasigeoid modelling

Abstract This study compares two interpolation methods in the problem of a local GNSS/levelling (quasi) geoid modelling. It uses raw data, no global geopotential model is involved. The methods differ as to the complexity of modelling procedure and theoretical background, they are ordinary kriging/least-squares collocation with constant trend and inverse distance weighting (IDW). The comparison itself was done through leave-one-out and random (Monte Carlo) cross-validation. Ordinary kriging and IDW performance was tested with a local (using limited number of data) and global (using all available data) neighbourhoods using various planar covariance function models in case of kriging and various exponents (power parameter) in case of IDW. For the study area both methods assure an overall accuracy level, measured by mean absolute error, root mean square error and median absolute error, of less than 1 cm. Although the method of IDW is much simpler, a suitably selected parameters (also trend removal) may contribute to differences between methods that are virtually negligible (fraction of a millimetre).