The XBT profiles are irregularly sampled in time. To minimize the analysis error and to obtain an interannual time series of bimonthly averages, an optimal estimation method is used. The theory of optimal interpolation, applied in meteorology ( initially by Gandin 1963 , is also used to analyse oceanographic data. The method used in this study ( temporal optimal averaging - OA ) was developed by Chelton and Schlax ( Chelton et al, 1991 ) .

The temperature data we used in the OA analysis, has the all data mean removed. After the Optimal Averaging, the mean is then added back to the OA temperature deviations.

From the OA temperatures thus obtained, the bimonthly anomaly is calculated, by removing the OA mean seasonal cycle. The final temperatures are then reconstructed, by adding to the interannual bimonthly anomaly, the seasonal bimonthly mean calculated directly from measured XBT's, and displayed in section 3.

To calculate the optimal averages, the following parameters are used :

Examples of the optimally averaged (OA) temperatures at 100m depth ( between 1988 and 1996), are compared to the raw XBT data sampled at that depth, in Figures 18 to 21 . The comparison shows that the OA temperatures underestimate the peaks and overestimate the troughs. The OA results improve substantially with better sampling, (compare Fig 18 and Fig 20 ) but still underestimate the maxima and overestimate the minima. This is due to a signal-to-noise ratio equal to 1. Where there are no XBT data, or very few, the OA gives a temperature value closer to the mean. This happens because the OA weights were not constrained to be unity in this study. Also, in some regions, the signal-to-noise ratio should be greater than 1 ( Phillips et al., 1990 ) . Since the OA statistics and the sampling rate vary over the years and along the XBT routes, the best compromise was thought to be a signal-to-noise ratio equal to one, throughout the study region.

OA time series of temperature sections are calculated for all lines, as described above. The interannual variation of SST, D20 and Dynamic Height ( 0/400 ) is plotted as bimonthly time series, at each grid point ( Figures 22 to 24 ) . Hovmoller diagrams are used to visualize the interannual anomaly of SST, D20 and Dynamic Height ( Figures 25 to 27 ). Dynamic height was calculated by slightly modifying the 'geopotential anomaly' function ('sw_gpan'), in Morgan's SEAWATER matlab library,( P. Morgan, 1994 ) .

NOTE : For lines IX-1 and IX-12, the interannual anomaly of D20, has the range of values reduced to the limits : -40 to 40, by replacing all anomalies greater than 40 with 40, and all anomalies less than -40 with -40. In doing so, a better contrast between the positive and negative anomalies is achieved. See Fig. 26 for lines IX-1 and IX-12. The reduction is done for illustration purposes only. The D20 anomaly data set, is not changed.