Ocean Interpolation by Four-Dimensional Weighted Least Squares—Application to the Waters around Australasia

Abstract

A new four-dimensional ocean interpolation system based on locally weighted least squares fitting is presented. A loess filter is used to interpolate irregularly spaced data onto a uniform grid. This involves projecting the data onto quadratic functions of latitude and longitude while simultaneously fitting annual and semiannual harmonics by weighted least squares. The smoothness scale of the mapping method adapts to match the data density, thus producing gridded estimates with maximum resolution. The filter has a vertical dimension, such that the data on adjacent levels are included in the computation. This greatly reduces the effects of discontinuities in data distributions between adjacent levels, since the estimates at each level are no longer independent. The loess scheme has been further modified so that the weighting of data points is adjusted to allow for the influence of both bathymetry and land barriers. This allows the bathymetry to influence the mapped fields in a natural way, reduces leakage of structure between deep and shallow regions and produces far more realistic coastal gradients. The flexibility of the loess approach has allowed further adjustments to compensate for irregularities in spatial and temporal sampling. The mapping is shown to be statistically consistent with an objective measure of the a priori noise of the dataset. Departures of the mapped fields from independent surface temperature climatologies and mean vertical sections derived from withheld expendable bathythermograph (XBT) data are within error limits. The method is applied to the major seas around Australia, New Zealand, Papua New Guinea, and Indonesia (508S‐108N, 1008E;‐1808) to form a high-resolution seasonal climatology of temperature, salinity, oxygen, nitrate, phosphate, and silicate, referred to as the CSIRO (Commonwealth Scientific and Industrial Research Organisation) Atlas of Regional Seas (CARS). Stringent quality control procedures have been applied to a comprehensive dataset assembled from all known sources. The resulting maps successfully resolve both the large-scale structure and narrow coastal features and illustrate how the bathymetry influences the property distributions.