The generalised cross validation method has been applied to the initial data set, and the the relocated data set for both stationary and unstationary methods. For the relocation, we used the optimal statistical parameters of the initial data set. We could imagine to use the modified statistical parameters of the relocated field to relocate the initial field, since it may contain more information than the initial one. This would lead to an iterative procedure, unless the statistical features of the relocated field are no more modified. At this stage, this method has not been implemented yet, and appears relatively expensive.
We must keep in mind that these parameters are global statistical estimators, and that they do not reflect particular statistical features of the hydrodynamic processes in the Alboran Sea.
Although after relocation, the global values obtained by GCV onto the whole domain might not correspond to particular local situations, in a smaller area, where the data distribution is more homogeneous, global and local estimators will.
Therefore, we chose to cross-validate the data set both in the
whole domain and in a particular sub-domain (-4 
to -3 longitude
and 35.5 to 36.5 latitude).
In the whole box (see figures 
to ),
we must keep in mind that regions are lacking data
even for the initial data set. The characteristic length for both T/S fields
ranges between 3 and 60 km, but essentially between 3 and 20 km.
The S/N ratio is smaller for the S field (0.001 to 0.1)
than for the S field ( 
), but relatively constant on depth.
The standard deviation is quite constant for both T/S fields, ranging between 1 and 2.
Also, we note that the relocation procedure essentially modifies the characteristic length.
In the case of the 'small box' (see figures to ,
the characteristic length is different, somtimes greater, sometimes smaller.
The S/N ratio is smaller in the first 100m for T and the standard deviation bigger for S.
These results are somehow disappointing and do not provide a clear interpretation. We may note that the shape of the cross validation estimator was found to be very flat and thus subject to numerical errors. Does it mean that the assumption of a sufficient data base is not valid to apply the GCV procedure to the data set. Or is the reference field not suitable? The optimal cross validation parameters should probably be computed in a box that is a compromise between the whole domain and the 'small box'.
This crucial step of calibration is of first importance and has to be improved.
Figure: L on the whole domain for temperature and salinity fields as a function of depth.
Figure: S/N on the whole domain for temperature and salinity fields as a function of depth.
Figure: Standard deviation on the whole domain for temperature and salinity fields as a function of depth.
Figure: L in the smallbox for temperature and salinity fields as a function of depth.
Figure: S/N in the smallbox for temperature and salinity fields as a function of depth.
Figure: Standard deviation in the smallbox for temperature and salinity fields as a function of depth.