Dissertation - HQ

74 Spatial distribution of larvae
Objective analysis
of the flow to reveal
its large scale direction
the displacement occurred along a straight line (which appears as a
safe assumption for a 22 s drift). Then, the drift vector was suppressed
from the velocity measured. Finally, instantaneous measurement were
averaged over the 4 min of recording. As the apparatus tended to drop
some data at depth, in each depth layer the mean was computed only
when more than four individual measurements were available. This
mean speed is used in the following.
Finally, to resolve the general direction of the flow field, CTD and
ADCP data were jointly interpolated through multivariate optimal
statistical interpolation (also called “objective analysis”) 178 . Dynamic
height was computed from CTD data, with a reference layer at 90 m.
This depth was sampled at all stations. At 90 m, the range of variation in
dynamic height between stations was small, around 0.3 dyn cm for all
rotations. In addition, deeper CTD records did not reveal any noteworthy
decline. Hence, 90 m was chosen as reference. CTD and ADCP data
were assessed independently and showed good agreement. Guided
by this agreement and previous studies 178–180 , the cross-correlation
parameter between the stream function and the geostrophic stream
function was set to 0.95, the divergence to total variance ratio to 0.05,
and the noise-to-signal ratio to 0.1. A critical parameter for the analysis
is the characteristic scale of the correlation function. Given the size of
the grid (ca. 10 km) there was no point in trying to resolve the structures
possibly generated by the atoll (size ca. 7-14 km) which are too small.
The characteristic scale was set to 25 km, which satisfied the requirement
of being at least twice the grid size and erased small scale variability
to reveal the global direction of the flow. The final interpolation grid
had square grid cells with 4 km sides and four layers corresponding to
the average depths of each of the four ascending MOCNESS nets (12.5,
37.5, 62.5, and 87.5 m).
4.2.3 Statistical analysis
Explicitly spatial
comparisons
For spatial analysis, the vertical dimension was not considered so, at
each station, the catches for nets 1-4 were pooled together. As the sampling
effort is not the same at all stations, abundances were divided by
volumes filtered to convert them to concentrations. When it was more
appropriate to deal explicitly with counts, concentrations were multiplied
by a constant volume, hence providing abundances which did not
suffer from bias in sampling effort, called “standardised” abundances.
Data was then analysed along two frameworks.
Spatial distributions of different families or ontogenetic stages were
compared two by two with Syrjala’s non-parametric test 181 . The method
tests for a difference between the distributions of two populations and
proceeds as follows. Consider a rectangle containing all K sampling
points, of coordinates (x k , y k ), k = 1, . . . , K. Divide the abundances (d)
of each population (subscripted i) by their total abundance, so that the