The horizontal scales are controled by introducing gaussian shaped horizontal covariances.
The error covariance matrix is computed at each step of the Kalman analysis. This matrix represents the progress made in the evaluation of the field, starting from the a-priori covariance as a first guess. The most objective expression of the quality of the estimation is the ratio of the a-posteriori to the a-priori variance. Fig. 2 shows the time mean of the relative error for temperature and streamfunction at two levels. The first level: 300 m, is above the zero crossing of the first baroclinic mode while the second level shown (1000 m) is located below The major part of the dataset provides constraints on temperature, and consequently this field is well estimated inside the array. The tomography constraints in particular produce lines of relative minima in the error maps. The quality of the estimation of temperature degrades in the deep layer. At this level the higher modes become important and they are not well resolved by the analysis. The streamfunction error is higher than the temperature error because it has more degrees of freedom: the barotropic mode and vertical salinity mode, and a smaller corresponding dataset. On the other hand we see little degradation with depth of the estimation of the streamfunction because of the clear predominance of the barotropic mode.
