Somerton et al.: The effects of wave-induced vessel motion on the herding of Limanda aspera 
25 
reduces either the size of the bridle contact area or 
the effectiveness of herding within the area will have 
a greater impact on the catch from the longer bridle 
and should result in a decrease in catch ratio. Thus, 
to determine whether herding is influenced by wave 
height, we used linear modeling (function 1m in R) to 
examine whether the catch ratio was significantly re¬ 
lated to wave height. 
Modeling the mechanism of wave influence on catch 
ratios of yellowfin sole 
vious studies of the survey trawl and its operation on 
yellowfin sole (Somerton and Munro, 2001); these are 
h= 0.58 and L off = 36 m. However, the estimate of L off is 
available only for standard length bridles, not the 2 
lengths used in our herding study. Consequently, as 
in the original study, we assumed L off is constant at 
all experimental bridle lengths, but only at zero wave 
height. At wave heights >0, we assumed that L off in¬ 
creases linearly with wave height, but at a rate that 
differs between bridle lengths. With these changes the 
wave-height-dependent herding model becomes 
We propose the following model to describe how the 
catch ratio could vary with wave height. Starting with 
the trawl catch model presented in Somerton et al. 
(2007), a trawl catch can be expressed as a function of 
trawl measurements (see Fig. IB for definitions) and 
other variables: 
C = k n (w n + h(w on ))DL, (1) 
where C 
w T 
w nr 
D 
L 
h 
catch in weight; 
net path width; 
width of the path contacted by the bridle; 
fish density; 
tow length; 
proportion of fish within the net path width 
that are captured; and 
proportion of fish within the bridle contact 
area that are herded into the net path. 
However, to better describe how sea state may affect 
the catch, it is simpler to express the relationship in 
terms of the bridle lengths and the bridle angle of at¬ 
tack (a). To do this, w on is redefined as 
w on = 2sin(a) (L bt -L ofr ) , (2) 
where L bt = bridle length including the length of the tail 
chain extensions connecting the doors to 
the bridles. The tail chain extensions used 
in the herding experiment were 12 m. 
L off = distance between the door and the point 
along the bridle where bottom contact is 
maintained 50% of the time; and 
a = bridle angle of attack. 
The angle of attack can be calculated for each tow as 
a = sin 
2 U, 
(3) 
Assuming that D and k n are approximately constant 
for each pair of tows, then the catch ratio (i?) can be 
expressed as 
R _ C‘ _ w n + /i(2sin(q)(L' bt - L off )) 
C s w n + /i(2sin(a)(L s bt -L off )) 
(4) 
where the superscripts l and s represent the long and 
short bridles. 
In this expression C 1 , C s , w n a, L* bt and L% t are mea¬ 
sured for every pair of tows, however h and L 0 f f need to 
be estimated by using data from separate experiments. 
Estimates of these parameters are available from pre¬ 
^ _ C 1 _ w n + 0.58(2sin(a)(L' bt -(36 + k'H))) .g, 
C s w n + 0.58(2sin(a)(L s bt ~(36 + k s H)))’ 
where H = the estimated wave height; and 
k\ k s = coefficients regulating the influence of wave 
height on L off for the long and short bridles. 
With this formulation, we are assuming that the only 
influence of wave height on herding is that of decreas¬ 
ing the length of the bridle in contact with the bot¬ 
tom, which happens differently for the long and short 
bridles. The choice in the form of the wave height ef¬ 
fect was, in part, guided by the results of the sea state 
and trawl performance study, which will be considered 
later. Note that when H= 0, L off becomes identical to 
the experimentally measured value and is identical for 
long and short bridle lengths. Therefore, the model has 
2 unknown parameters; that is, k l and k s . To estimate 
these parameters we considered the right side of the 
above equation as a predicted value of the catch ra¬ 
tio and minimized the sum of the squared differences 
between the observed and predicted catch ratios over 
the 18 paired tows, using nonlinear minimization (R 
function nlm). 
Variation in survey abundances of yellowfin sole with 
wave height 
The abundance of yellowfin sole in the EBS survey area 
is estimated annually with the EBS survey by using 
the swept-area method applied to each of the 356 sta¬ 
tions located at the centers of a rectangular sampling 
grid (Conner and Lauth, 2016). Annual abundance is 
estimated by multiplying the estimates of local density 
(i.e., catch/trawl swept area) by the area of each grid 
square and then summing over all grid squares. A vari¬ 
ety of environmental parameters are also measured at 
each sampling site, including swell and wave heights 
estimated by the vessel captain, which again were 
summed and referred to as wave height. Although the 
survey time series began in 1982, the wave height data 
have only been available since 2005. For each year of 
data, wave height was averaged over all sampling sites 
where yellowfin sole were caught. 
To determine whether the abundance estimates from 
the yellowfin sole survey were influenced by variation 
in wave height, perhaps because wave height influ¬ 
enced trawl sampling efficiency, we modeled the sur¬ 
vey abundance estimates as a linear function of mean 
