Local polynomials for data detrending and interpolation in the presence of barriers

We discuss features of local polynomial interpolation (LPI), focusing on the problem with unstable solutions of the LPI system of linear equations. We develop a new diagnostic based on condition number values. Also, a variant of Tikhonov regularization is proposed, which allows the production of continuous predictions and prediction standard errors nearly everywhere in the data domain. This variant of LPI can be used in the presence of barriers defined by polylines. LPI model is a good candidate for real time automatic mapping of the data regularly collected from the environmental monitoring networks. We illustrate the LPI usage with both simulated data and real data.