816 
U. Callies et al.: Surface drifters in the inner German Bight 
Ocean Sci., 13, 799-827, 2017 
www.ocean-sci.net/13/799/2017/ 
A couple of different processes can be relevant for an ex 
change of energy and momentum between surface waves 
and underlying mean currents (Smith, 2006). Under open 
sea conditions, probably the most important process affect 
ing near-surface drifters is the Stokes drift which arises when 
backward motions beneath the troughs of surface gravity 
waves do not fully compensate forward motions beneath the 
crests. However, a key observation from our simulation ex 
periments is that for surface drifters the inclusion of an ex 
plicitly simulated Stokes drift did not produce an added value 
beyond a simple parametrization of wind drag in terms of 
10 m winds. According to Fig. 10b, wind speeds used as forc 
ing for either TRIM or BSHcmod are both highly correlated 
with Stokes drifts calculated with wave model WAM (based 
on the same wind hindcast also used as forcing for TRIM). 
This similarity agrees with results reported by Drivdal et al. 
(2014, their Fig. 7), for instance. 
From experimental data, Rohrs et al. (2012) estimated 
Stokes drift to be about twice as large as effects of direct wind 
drag. However, as the roles of direct wind drag and Stokes 
drift are difficult to disentangle, we did not conduct experi 
ments with mixtures of the two processes. For the factors a or 
/3, we chose in Eq. (1), drift components from either windage 
or Stokes drift were similar most of the time (Fig. 6). Vali 
dating modelled wave effects based on four surface drifters 
deployed near the Grand Banks (Newfoundland), Tang et al. 
(2007) considered both processes in combination. They also 
found simulated Stokes drift to be linearly related to wind 
velocities, so that it seems difficult to decide whether the ap 
proximately 21 % decrease of separation between modelled 
and observed trajectories after 1 day are really attributable to 
Stokes drift effects. According to Breivik and Allen (2008), 
the impracticality to separate Stokes drift effects from an em 
pirically parametrized direct wind drag is a major reason why 
Stokes drift is neglected even in most operational search and 
rescue modelling systems, where a realistic assessment of ex 
isting uncertainties and their origin is of utmost importance. 
Tang et al. (2007) found Stokes drift to be about 1.5 % of 
wind speed; Li et al. (2017) report a value of 1.6 %. These 
values agree with the ratio (0.3/20) of the scales annotated 
on the two y coordinates in Fig. 10b. For low wind condi 
tions, the relative importance of Stokes drift decreased (again 
in agreement with the results of Tang et al., 2007), but in 
these cases the overall contributions from winds and waves 
are small anyway. 
In particular, growing young wind seas forced by local 
winds typically produce strong surface Stokes drifts that de 
cline fast with depth (e.g. Rohrs et al., 2012). Breivik et al. 
(2016) developed an approximate method to efficiently cal 
culate this near-surface shear, underestimated by the com 
mon assumption of a monochromatic profile. Based on these 
formulas, Rohrs and Christensen (2015) calculated in the 
context of a drifter experiment in the Barents Sea and Nor 
wegian Sea that an average Stokes drift of 8.9 cms -1 at 
the surface contrasted with an average of 3.7cms -1 at 1 m 
depth. For the present study, we neither applied theoretical 
profiles nor conducted an in-depth model calibration. How 
ever, in the light of the above numbers, the 50 % factor a in 
Eq. (1) we chose for BSHcmod+ S seems to be a reason 
able value for drifters representing a surface layer of about 
1 m depth. Vagueness of the factor corresponds with that of 
the 0.6 % windage factor /3 used in BSHcmod + W. Given 
the limited data, in both cases, even most careful calibration 
would not lead to robust estimates. The criterion we applied 
for selecting a or (3 is that the overall eastward displace 
ment of a drifter’s location should roughly agree with that 
observed. A convincing confirmation of our selection was 
that the strength factors we chose worked consistently well 
for all drifters. 
Similarity between simulations with either wind drag or 
Stokes drift (see SM4) is an implicit consequence of how 
parameters were chosen. According to Fig. 6, a period with 
major differences between contributions from either windage 
or Stokes drift occurs during days 30-34, when indeed simu 
lations based on BSHcmod + W and BSHcmod + S, respec 
tively, diverge (see Figs. A2 and A3). According to Fig. 4b, 
however, results from model version BSHcmod + W seem to 
be more realistic. It is interesting to see that also TRIM sim 
ulations are particularly wrong in this period, producing, e.g. 
for drifter no. 5 transports to the south-east (Fig. A4b), when 
in reality the drifter moved in a north-east direction (Fig. 4b). 
Figure 12 compares magnitudes of observed and simulated 
drift speeds on an hourly basis, referring to trajectories of 
drifter nos. 5 and 6 during days 0-17 (see SM5 in the Sup 
plement for corresponding full time series). As in Fig. 6, all 
simulated velocity components were specified at observed 
rather than simulated drifter locations (i.e. no drift simulation 
was performed), so as to avoid the problem of spatial sepa 
ration between simulations and observed counterparts. Ob 
served and simulated drift speeds agree surprisingly well at 
least during approximately days 0-12. Nearly perfect agree 
ment for one drifter sometimes coincides with discrepancies 
for the other, a possible manifestation of sub-grid-scale pro 
cesses (see observations at the beginning of day 5, for in 
stance). 
Together with total drift speeds, Fig. 12 also shows mag 
nitudes of simulated windage and Stokes drift. During most 
of the time, these two drift components are of similar size. 
More short-term pulses of Stokes drift can be discerned on 
days 5-6. Generally, however, contributions from both wind 
and waves are smooth. A removal of compensating tidal ef 
fects by averaging enhances visibility of the contributions 
of winds or waves (see Fig. 6). Note that, due to vectors 
having different directions, differences between total drift 
speeds and contributions of windage do not directly trans 
late into magnitudes of mean Eulerian currents. For instance, 
a non-zero windage effect may be offset by an opposed Eu 
lerian current. For BSHcmod + W simulations of drifter no. 
5, we found average magnitudes of hourly Eulerian cur 
rents to be about 0.27ms -1 and corresponding values for