# Darryl Williams

##
Influence of the Wind on the Motion of Surface Drifters: Application of a Data Assimilative Model to the Outer Scotian Shelf

### Thesis Approved 1996

The dynamics of the upper meter or so of the ocean are complicated by
the interaction of current shear, wind shear and the action of waves.
An effective model for the motion of surface drifters should take into
account: (i) Stokes drift; (ii) the leeway effect, due to wind acting
on exposed areas of the drifter; (iii) motion in the wind drift layer,
which consists of a 5cm thick surface sublayer above a logarithmic
sublayer of about one meter thickness. Drifter trajectories were
observed on the outer Scotian Shelf in May 1993. Three types of
drifter were deployed: one was drogued at 20m, the other two were
surface drifters with different drafts and mast areas. To quantify
the various components of the drifter motion, the water column was
partitioned into separate layers leading to the following expression
for drifter velocity:
Udrifter = Udeep + UEkman + UStokes + Ulee + Ulog + Uerror

Udeep is the background flow and UEkman is the velocity near the top
of the Ekman layer. The remaining suB.Sc.ripts refer to the surface
corrections for Stokes drift, the leeway effect, and the logarithmic
sublayer (the effect of the surface sublayer was assumed negligible).
The calculation of UStokes, Ulee and Ulog is straightforward and based
on physical principles. The background flow (below 20m) was modelled
using the adjoint method to assimilate current data from moored
instruments and a shipborne acoustic doppler current profiler. UEkman
was modelled statistically, using complex regression. The background
flow correction gave the greatest reduction in the variance between
model and observation of the drifter velocities. The variance of the
error was 53% that of the observed (i.e. uncorrected) velocity
variance. Subtracting the surface correction factors further reduced
the residual variance to 45%. Complex regression of the corrected
drifter velocity on the wind stress reduced the residual variance to
37%.