Sound speed was calculated using the Del Grosso formula [Del Grosso, 1974]. The average sound speed profile is used as the reference state in the inversion. Sound speed anomalies (δC) in the horizontal and vertical are represented by truncated Fourier series and empirical orthogonal functions (EOFs), respectively [Howe et al., 1987; Gaillard, 1992]. The a priori variance of δC is determined for the tomography site, using the NODC data. The spatial covariance function of δC is assumed to have a Gaussian distribution with a 150km correlation length based on TOPEX/ POSEIDON altimeter data [Kuragano, 1997, personal communication].
The first 4 EOFs (representing 99 percentage of the DC variance) are used, and the high wavenumber cutoff for the Fourier series is set to 1 cycle/240km (the longest path is 1013.8km) in order to resolve mesoscale eddies. The δC field, thus, can be reduced to a model with a finite number of discrete parameters. The root mean square (rms) travel time uncertainty is set at 20ms to take into account errors in travel time measurements as well as inadequacies in the parametrized model.
Three-dimensional sound speed fields reconstructed by the inversion are converted into temperature fields using a simple sound speed formula [Mackenzie 1981]. The expected rms uncertainty of the inversion for temperature takes a maximum value of 0.3℃ near the thermocline between 250m and 350m depths (compared to the a priori expected variation of 4.1℃), and about 0.1℃ at depths greater than 700m (compared to the a priori expected variation of 1.7℃); the fraction of unresolved variance is 7.3% at 300m depth and 5.9% at 700m depth. The uncertainly of the result is caused by a combination of data errors, the nonlinearity between the reference and actual sound field that contains lateral inhomogeneities [Spiesberger, 1985], the finite number of discrete parameters that describe the ocean model, the limited precision of travel time measurements, and the insufficient spatial coverage of ray paths.
Results
The time evolution of the estimated range-averaged sound speed anomaly from the reference profile is shown in Figure 3(a). The three months of data for the path T5-T2 (1000.4km range) running along the T/P track p238 (see Figure 1) are ploted. The sound speed anomaly shows the drastic changes to have a maximum on July 27 (marked A), minimum on August 10 (marked B) and maximum on August 31 (marked C), indicating a temporal variability of about a one-month period. The warming event occurring from the end of August to the beginiing of September is especially pronounced.
A prominent feature for a vertical temperature section between stations T2 and T5 obtained by the XCTD/CTD hydrocasts from July 20 to July 22, 1997 is that there are large temperature gradients of isotherm s from 200m to 1000m near station T5; this is the Kuroshio front (Figure 3(b), dashed lines). A convex lens-shape water mass with a horizontal scale of about 150-km centered at 400m depth is visible near 31°N (650km from station T5) as seen with the isotherms of 14-16 ℃. This water mass which may be a subsurface warm eddy influences the entire water column. A cold water mass with temperatures less than 4 ℃ and a depth range of 100m intrudes into the 400m layer around station T5.
