Some Remarks on Interpolation of Nonstationary Oceanographic Fields

The performance of four methods for interpolating anisotropic, spatially nonstationary fields is examined. The methods are optimal interpolation (OI, also known as objective analysis), spline interpolation, multiquadric-biharmonic method (MQ-B), and the inverse distance weighted method. The tests were performed using multiple realizations of random bivariate fields with known 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 from an increase in data density. In contrast, interpolation methods such as spline and MQ-B, which adjust the frequency response characteristics so that the passband of the filter increases as the data spacing decreases, will account for such spatial variations and provide a more accurate interpolation. In the case of nonstationary and highly anisotropic processes, the most accurate interpolation analysis was obtained by spline interpolation and MQ-B. As a result of the nonstationary fields encountered in the section crossing the ACC, the interpolation skill of the multiscale OI algorithm with an isotropic covariance function was lower. The highest relative interpolation errors were obtained in the case of regular gaps resulting from interspersed deep and shallow stations, even though the total number of retained data points is almost 80%. This is a consequence of inadequate sampling. All considered methods do a poor job of extrapolating data in boundary regions. For the ACC mapping, extrapolation errors exceeded the standard deviation of the fields by several times, indicating that the results of any interpolation method should be considered very critically in the boundary regions.