A Case Study in Three-Dimensional Inverse Methods: Combining Hydrographic, Acoustic, and Moored Thermistor Data in the Greenland Sea

Abstract

A variety of measurements, including acoustic travel times, moored thermistor time series, and hydrographic stations, were made in the Greenland Sea during 1988–89 to study the evolution of the temperature field throughout the year. This region is of intense oceanographic interest because it is one of the few areas in the world where open-ocean convection to great depths has been observed. This paper describes how the various data types were optimally combined using linear, weighted least squaws inverse methods to provide significantly more information about the ocean than can be obtained from any single data type. The application of these methods requires construction of a reference state, a statistical model of ocean temperature variability relative to the reference state, and an analysis of the differing signal-to-noise ratios of each data type. A time-dependent reference state was constructed from all available hydrographic data, reflecting the basic seasonal variability and keeping the perturbations sufficiently small so that linear inverse methods are applicable. Smoothed estimates of the vertical and horizontal covarinces of the sound speed (temperature) variability were derived separately for summer and winter from all available hydrographic and moored thermistor data. The vertical covariances were normalized before being decomposed into eigenvectors, so that eigenvectors were optimized to fit a fixed percentage of the variance at every depth. The 12 largest redimensionalized eigenvectors compose the vertical basis of the model. A spectral decomposition of a 40-km correlation scale Gaussian covariance is used as the horizontal basis. The uncertainty estimates provided by the inverse method illustrate the characteristics of each dataset in measuring large-scale features during a diversely sampled time period in the winter of 1989. The acoustic data alone resolve about 70% of the variance in the three-dimensional, 3-day average temperature field. The hydrographic data alone resolve approximately 65% of the variance during the selected period but are much less dense or absent over most of the year. The thermistor array alone resolves from 10% to 65% of the temperature variance, doing better near the surface where the most measurements were taken. The combination of the complete 1988–89 acoustic, hydrographic, and thermistor datasets give three-dimensional temperature and heat content estimates that resolve on average about 90% of the expected variance during this particularly densely sampled time period.