19. Results are from 16 collocated tans-Pacific XBT surveys over a 4-year period concurrent with theTOPEX/PDSIDON altimetric mission Sparse salinity data were also collected and used to determine the salt contribution to sea level anomaly (J. Gilson, D. Roemmich, B . Cornuelle, and L.-L. Fu, J. Geophys. Res., in presss).
20. C. Wunsch, The Ocean Circulation Inverse Problem (Cambridge Univ. Press, New York, 1996); R. Daley, Atmospheric Data Analysis (Cambridge Univ. Press, New York, 1991).
21. I. Fukumori, J. Geophys. Res., 100, 25,027 (1995); D. Stammer and C. Wunsch, J. Geophys. Res., 101, 18,409 (1996); D. Menemenlis and C. Wunsch, J. Atmos. Oceanic Technol., 14, 1420(1997).
22. The estimation results and their uncertainty are functions of the prior covariance matrices for the system and measurement errors. Here we use diagonal, time-independent, prior covariance matrices for model error covaiance and for the altimetric observation covariance. The model error covariance has a variance consistent with the variance of GCM-hydrographic differences in the North Pacific. The observation error matrix has a variance of 9cm2, which includes altimeter noise (1cm2) and barotropic-salinity model errors (8cm2). For acoustic data, a full covariance is derived based on the seasonal climatology15 and on the particular transmission characteristics along each section. D. Menemenlis and M. Chechelnitsky. (Mon. Weather Rev., in press) discuss model and data errors in more detail. The assimilation results are sensitive to the specification of the errors, including spatial and temporal scales.
23. W. B. White and C.-K. Tai, J Geophys. Res., 100, 24,943 (1995); J. Hsiung, R. E. Newell, and T. Houghtby, Nature, 325, 518(1987).
24. B. D. Dushaw, P. F. Worcester, B. D. Cornuelle, and B. M. Howe, J. Phys. Oceanogr., 23, 2650 (1993).
25. The meteorological analyses are not accompanied by an error bar for the estimated air-sea heat flux, and this absence is a major obstacle to further quantitative progress in many climate problems. A recent estimate [J. R. Moisan and P. P. Niiler, J. Phys. Oceanogr., 28, 401 (1998)] confirms that bulk formula errors probably lie in the range of 20 to 40W/m2; these errors may well be systematic.
26. Acoustic thermometry owes its development to continuing support by the Office of Naval Research. This work was also supported by the Strategic Environmental Research and Development Program through the Defense Advanced Research Projects Agency, the Department of Energy, and NASA and by grants of computer time from project SCOUT at the MIT Laboratory for Computer Science. The original version of this paper appeared in ATOC Consortium, Science, 281, 1327 (1998).
