Observations, be they acoustic or altimetric, can be viewed as measuring the departure of the GCM prediction from the real ocean. The measurements define the model-data difference. The “observation” matrix specifies the relation between model elements and the observations, and the measurement error is assumed to have zero mean with known covariance.
Those elements of the model that are uncertain (including initial and boundary conditions and inadequate physics) lead to errors in calculating the oceanic state that are detectable in the observations, thus permitting correction of the model elements. Conversely, for those elements of the oceanic state that are poorly observed or not observed at all, the model will provide a realistic estimate, and the combination of the model and the data produces a better estimate than either could alone.
We use a scheme21 based on linear estimation theory and on a coarse resolution representation of the model error consisting of four vertical temperature modes, 8｡?amples in the horizontal, and monthly samples in time. Smaller, unresolved scales as well as salt and barotropic effects become part of the observational noise, and their dynamical consequences are accounted for in the model error terms; that is, observation and model errors now include the deficiencies in the reduced-state linear model as well as those in the GCM. A priori covariances for the various problem unknowns are based upon the comparisons already described.22
CIRCULATION AND HEAT BUDGET
The above model-data combination produces a best estimate of the heat content, barotropic, and salinity changes. Comparison of the January 1996 to January 1997 temperature change predicted by the GCM alone (Fig. 4, top panel) to that predicted by the GCM-altimeter-acoustic combination (Fig. 4, bottom panel) shows that the GCM alone approximately simulates interannual variations in heat content changes, for example, the broad diagonal bands of warmer and colder water crossing the basin from southwest to northeast. But, in general, the GCM underestimates the magnitude of these change, which can be as large as 0.2℃ averaged over the top 4000m. Changes in the current fields reflect large (up to 5cm/s at 610-m depth) fluctuations in the tropical Pacific velocity field (Fig. 4). Substantial interannual changes are also observed at midlatitudes, away from the relatively quiet northeastern Pacific. About 50% of the sea level variance on time scales of months to years and spatial scales exceeding about 1500km is contributed by the change in heat content. Altimetric-acoustic differences apparently result from a barotropic mass redistribution, with variable salt anomalies a contributing, but smaller, factor.
The top-to-bottom heat content anomaly in the region spanned by the ATOC array, 168°to 240°E, 16° to 56°N, when converted to equivalent sea surface heat flux (Fig. 5), shows that the GCM underestimates the strength of the seasonal cycle compared to the combined GCM-altimeter-acoustic estimate. This deficiency, present in almost all state-of-the-art ocean models, results from missing information on the mixed-layer physics and errors in the surface boundary conditions. The heat budget23,24 of this region can be further elucidated by comparing these heat content estimates to the surface heat flux determined from meteorological analyses. Assuming that the two estimates are perfect, their difference would be proportional to the advective component of heat flux entering the region. If atmospheric estimates of direct heat transfer are reliable to ±30W/m2,25 the difference indicates a surprisingly large3 seasonal cycle in the advective components (180W/m2 peak-to-peak surface equivalent). The result is consistent in magnitude and phase with previous tomographic estimates24 of 50 to 150W/m2 advected into a triangle centered at 160°W and 35°N.
