Application of Thin-Plate Splines in Two Dimensions to Oceanographic Tracer Data

Abstract

his study explores the utility of the thin-plate spline (TPS) as a mapping procedure for oceanographic sections of bottle data in comparison with objective mapping (OM), sometimes referred to as objective interpolation. Standard OM techniques in oceanography require a priori assumptions about the structure of the errors associated with mapping when interpolating irregularly spaced data. Alternatively, the TPS can be used to approximate mapping errors by fitting a nonparametric model using multiple covariates with a less rigid, physically consistent, spatial correlation structure. The case is made that these errors reflect the sparsity of the data coverage and quantify mapping error better than the estimates using OM. It is demonstrated that the maps from the TPS recreate the essential large-scale features of chlorofluorocarbon- or freon-11 (CFC-11) concentrations and inferred ?ages,? but smooth over smaller-scale features, such as eddies. The TPS can outperform OM when either the distance between the samples is larger than the correlation length scale or the signal-to-noise ratio is small. With more data, OM and TPS estimates yield increasingly similar results, but differ most markedly where there are extrema in the mapped fields, particularly at the domain boundaries. The TPS is recommended over OM when the spatial domain is sparsely sampled but the full range of covariates is known to be spanned by these samples.