Some remarks on interpolation of nonstationary oceanographic fields

The performance of four methods for interpolating anisotropic, spatially no nstationary fields is examined. The methods are optimal interpolation (OI, also known as objective analysis), spline interpolation, multiquadric-bihar monic method (MQ-B), and the inverse distance weighted method. The tests we re performed using multiple realizations of random bivariate fields with kn own underlying statistics, as well as highly anisotropic and nonhomogeneous temperature and salinity fields across the Antarctic Circumpolar Current ( ACC). The results of tests using homogeneous random fields show that all methods except the inverse distance method have similar performance in the accuracy . When the interpolated field is sampled adequately and data distributions are dense, the presence of spatial deviations of the field statistics from the field average will limit the interpolation skill of OI to be gained fro m an increase in data density. In contrast, interpolation methods such as s pline and MQ-B, which adjust the frequency response characteristics so that the passband of the filter increases as the data spacing decreases, will a ccount for such spatial variations and provide a more accurate interpolatio n. In the case of nonstationary and highly anisotropic processes, the most acc urate interpolation analysis was obtained by spline interpolation and MQ-B. As a result of the nonstationary fields encountered in the section crossin g the ACC, the interpolation skill of the multiscale OI algorithm with an i sotropic covariance function was lower. The highest relative interpolation errors were obtained in the case of regular gaps resulting from intersperse d deep and shallow stations, even though the total number of retained data points is almost 80%. This is a consequence of inadequate sampling. All con sidered methods do a poor job of extrapolating data in boundary regions. Fo r the ACC mapping, extrapolation errors exceeded the standard deviation of the fields by several times, indicating that the results of any interpolati on method should be considered very critically in the boundary regions.