Surface drift error estimation

The estimation of the error due to the surface drift, before the first position and after the last one, can be done only for those floats containing all the necessary data. This is just an estima-tion of the error, it cannot be used to correct

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Figure 2.5: Histogram of the relative error in the deep velocity estimate due to the combination of the untracked surface drift and the horizontal drift during the float’s vertical migration.

The top and bottom panels respectively show the zonal and latitudinal velocity components.

the original data.

To estimate the real position when the float arrives to the sea surface, we calculate the time between the surface arrival and the first trans-mitting position, and assume that during that time lapse the float moves with the same mean velocity calculated from the first and the last surface positions at surface. Subtracting this displacement from the first position, we can es-timate the position where the float actually ar-rived to the sea surface.

The method to estimate the real sinking posi-tion is similar, but using the time lapse between the last position and the start of the descend-ing profile. Assumdescend-ing again that, durdescend-ing this time interval, the float moved with the calcu-lated mean surface speed, and adding this dis-placement to the last position, we can recon-struct the actual position where the descending profile started.

The difference between the velocity calcu-lated from the original and corrected positions is assumed to be the error introduced in the deep velocity calculation by the surface drift of the float during the interval between the arrival to the surface and the first transmission position, and between the last transmission position and

the start of the descending profile.

In addition, not all the available data is valid: the status of the dates is flagged depend-ing on whether the date has been estimated, extracted from the metadata, transmitted by the float, or is unknown. For our purposes only those dates which have been transmitted by the floats can be used. Therefore, we keep only those data with values flagged as “2” in the STATUS variable. The presence of cor-rect data, both for JULD ASCENT END and JULD DESCENT START, is confirmed for only 75066 cycles of the total 780809 surface veloc-ity data values. Therefore, only 9.6% of the to-tal velocity data contains enough information to estimate the error due to surface drifting that cannot be tracked. The mean time gap be-tween the arrival to the sea surface and the first position (Fig. 2.3) is 31 minutes (less than 1 hour in 84% of the profiles), and the mean time gap between the last float’s position and the im-mersion time (Fig. 2.4) is 1 hour 21 minutes (less than 2 hours in 77% of the profiles). An analogous procedure can be followed to correct the parking depth velocities. The first step is to correct the error associated to the untracked surface drift; knowing the duration of the

sur-Figure 2.6: Geographical distribution of the profiles contain-ing all the necessary variables to estimate the surface drift error.

face drifts and assuming the float moves with the mean surface velocity before the first transmis-sion and after the last one, we can estimate the real emersion and immersion positions and re-calculate the floats deep velocity. The difference between this corrected velocity and the previous velocity estimate is considered as an estimate of the deep-velocity error due to the surface drift.

This surface drift introduces a small error which in approximately 70% of the cases is less than 10% of the deep velocity value, and in 95% of the cases is less than the deep velocity value, this re-sult applying for both velocity components.

To have an estimation of the total error, we add the error caused by the untracked surface drift to the error associated to the horizontal

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drift during the vertical migration (Lebedev et al., 2007). The overall error appears to be less than 10% of the deep velocity value in approx-imately 50% of the profiles, and in 92% of the profiles it is smaller than the deep velocity value for both components of the deep velocity (Fig.

2.5). In particular, the mean error contribution due to the surface drift is much smaller than the error due to the horizontal drift during the ver-tical migration.

The calculation of the surface drift error is possible only for those profiles where the pre-viously mentioned variables are present, Figure 2.6 shows the distribution of the profiles where this is possible. Despite there is no global cover-age, the distribution is wide enough to confirm that our estimates are reliable for the whole data set. It is important to remember that these es-timations are only for a relative small number of vectors; they provide an estimate of the error but cannot be used for correcting the velocity fields.

2.6 Non-instrumental error sources