The amplitude of ηacoust at the aunual period is, on average, half that of ηaltim. Similarly ηXBT, which is consistent with the acoustic data during the overlapping period, has an rms difference from ηaltim of 2.9cm, larger than likely errors in the altimetric measurements (〜1cm rms) and XBT measurements (0.2cm rms for the 800-m thermal contribution).17 A small number of salinity measurements along section v1 suggest a considerable (〜2cm rms) salt contribution to η on seasonal to interannual time scales, especially in the transition zone between the low-salinity waters of the California Current and the saltier subtropical waters offshore.
Short period fluctuations in ηaltim and ηGCM are primarily caused by wind-forced barotropic Rossby waves. These waves are not sensed either by the acoustic18 or by the temperature measurements. A study19 comparing XBT and altimetric data over a period of 4 years along a trans-Pacific section concluded that approximately 80% of the variance of ηaltim and ηXBT was coherent at wavelengths of 500 to 3000km, which could be interpreted as implying a barotropic variance contribution of about 20%.
Insufficient information exists to separate fully the salt, thermal, and mass contributions to the low-frequency sea level anomaly from data alone,6 but a partial estimate can be obtained from the GCM prediction. Of the total GCM sea level variability in the ATOC region, 28% lies in the barotropic mode at periods exceeding a few months, and this serves as our a priori estimate of low-frequency mass contributions to ηaltim. All estimates of sea level variability are consistent if 1/3 to 1/2 of the low-frequency variance is contributed by processes not reflecting heat content changes.
MODEL-DATA COMBlNATIONS
Because the observations and the model produce independent estimates of the oceanic fluctuations with distinctly different expected errors, we can attempt a statistical best estimate of the oceanic state through their formal combination. 20 The true oceanic state vector is defined as a set of physical quantities (typically velocity, temperature, salinity, and surface pressure) on a three-dimensional grid that, along with initial and boundary conditions, provides sufficient information to calculate the oceanic state one time step in the future. Estimates of the ocean state differ from the true state because of unknown initial and boundary conditions, indeterminate model parameters (for example, mixing coefficients), and other errors in the physics of the model. We assume that the second-moment matrix of these errors is at least approximately known.
