Tuning interpolation methods for environmental uni-dimensional (transect) surveys

The paper proposes rCV, a new randomised Cross Validation (CV) criterion specially designed for use with data acquired over non-uniformly scattered designs, like the linear transect surveys typical in environmental observation. The new criterion enables a robust parameterisation of interpolation algorithms, in a manner completely driven by the data and free of any modelling assumptions. The new CV method randomly chooses the hold-out sets such that they reflect, statistically, the geometry of the design with respect to the unobserved points of the area where the observations are to be extrapolated, minimising biases due to the particular geometry of the designs. Numerical results on both simulated and realistic datasets show its robustness and superiority, leading to interpolated fields with smaller error.