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Morawitz, WML, Cornuelle BD, Worcester PF.  1996.  A case study in three-dimensional inverse methods: Combining hydrographic, acoustic, and moored thermistor data in the Greenland sea. Journal of Atmospheric and Oceanic Technology. 13:659-679.   10.1175/1520-0426(1996)013<0659:acsitd>;2   AbstractWebsite

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 held 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 squares 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 !he basic seasonal variability and keeping the perturbations sufficiently small so that linear inverse methods are applicable. Smoothed estimates of the vertical and horizontal covariances 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 bring 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.

Cornuelle, BD, Morris MY, Roemmich DH.  1993.  An Objective Mapping Method for Estimating Geostrophic Velocity from Hydrographic Sections Including the Equator. Journal of Geophysical Research-Oceans. 98:18109-18118.   10.1029/93jc01729   AbstractWebsite

Objective mapping can remove the equatorial singularity from the problem of estimating geostrophic shear from noisy density measurements. The method uses the complete thermal wind relation, so it is valid uniformly on and off the equator. Errors in the thermal wind balance are due to neglected terms in the momentum balance, which are treated as noise in the inverse problem. The question of whether the geostrophic balance holds near the equator is restated as a need to estimate the size of the ageostrophic noise in the thermal wind equation. Objective mapping formalizes the assumptions about the magnitudes and scales of the geostrophic currents and about the magnitudes and scales of the ageostrophic terms and measurement errors. The uncertainty of the velocity estimates is calculated as part of the mapping and depends on the signal to noise ratio (geostrophic density signal to ageostrophic ''noise'') in the data, as well as the station spacing and the scales assumed for the geostrophic velocities. The method is used to map zonal velocity from a mean Hawaii-Tahiti Shuttle density section. These are compared with previous velocity estimates for the same dataset calculated using other techniques. By choosing appropriate scales, the objective map can duplicate previous results. New temperature data are presented from a repeating, high-resolution expendable bathythermograph section crossing the equator at about 170-degrees-W with four cruises a year between 1987-1991. There appear to be significant differences between this mean temperature and the shuttle mean temperature. Temperature is converted to density with the aid of a mean T-S relation and geostrophic velocity maps are calculated for the 4-year mean. The mean geostrophic undercurrent obtained from our sections is weaker than in the shuttle estimate and is centered slightly north of the equator. Enforcing symmetry about the equator removes the offset of the current, giving a stronger, but narrow undercurrent. The density field apparently includes significant (O(0.5 kg M-3)) large-scale ageostrophic variability which makes velocity estimates from single cruises poorly determined near the equator.

Dushaw, BD, Worcester PF, Cornuelle BD, Howe BM.  1993.  Variability of Heat-Content in the Central North Pacific in Summer 1987 Determined from Long-Range Acoustic Transmissions. Journal of Physical Oceanography. 23:2650-2666.   10.1175/1520-0485(1993)023<2650:vohcit>;2   AbstractWebsite

The evolution of the heat content in the central North Pacific Ocean during summer 1987 has been measured using acoustic transmissions between transceivers deployed in a triangle approximately 1000 km on a side. The acoustically determined heat contents of the source-receiver sections agree with heat contents computed from CTD and XBT data obtained during May and September 1987. The accuracy of acoustical measurements of range-averaged heat content is comparable to estimates from CTD and XBT data. Transmissions at four-day intervals allow the continuous observation of heat content and show that it varies on time scales of weeks or less. The magnitude of these variations is of the same order as that observed from XBT sections, which are only occasionally available. Ocean-atmosphere heat exchange from bulk formulas accounts for only about half of the observed heat content increase from May through September 1987, indicating that advective effects are important in the region. The excess heat change is calculated to be of order 50-150 W m(-2). The advective component of the near-surface heat budget is roughly in phase with the surface flux component.