Explication of relation between fishery and vortices
using 3-D visualization
Takashi Uenaka 1, Koji Koyamada 1
1Institute for the Promotion of
Excellence in Higher Education, Kyoto University, Japan

1. Introduction
The ocean ecosystem such as the marine resources andhabitation quantity keeps changing for dozens of years. The
typical example is "fish species change" which recent climatic
variation such as global warming causes.
For such change, the fishermen often fail to find theirfishery spot, which had not occurred before. That means a vain
consumption of oils caused by the failure. It is sure that thefishery distribution has been different from what it had been.
Thus, it is required that we need to pinpoint the fishery spot by ahigh-precision ocean model assimilated by observation datasets.
In this article, we focus on the neon flying squids which is in
the middle of the ocean food chain resources. It is observed thatthe fishery spots of the saury fish often are located near a subtle
vortex, whose diameter is about 10km [1]. The vortices are often
found around a small vortex [1], whose diameter is about 100200km. The saury fish is also a kind of fish migration as thesame as the neon flying squids. We assume that the observationis also true for the neon flying squids.
Although the experience of the fishermen indicates that thefishery of the neon flying squids is located near the vortex, therelation between the vortex and the fishery had not been madeclear so far. Our main target is in the offing of the Aomori North
Pacific sea. The fishery can be characterized by using an indexof catches per unit effort (CPUE).
In this article, we apply the critical point theory to thesimulation results using the high-precision ocean model in order
to explore the vortices. In the critical point theory, we firstsearch for the critical point where the velocity vanishes and thenclassify the critical point by calculating the eigenvalues of thevector gradient tensor.

The velocity vector can be linearly approximated by its firstorder Taylor expansion as shown in equation 2.1. Here we
describe the vector gradient tensor as J.

uvw

xyzuxvxw
xuyv
yw
yuz xvyzw zzx
J yz(2.1)

2.2 Classification of the Critical point
In the critical point theory, the critical point can be classified
by the eigenvalues of the vector gradient tensor, J [2]. The
critical point can be classified as a vortex center if a pair ofcomplex conjugate numbers is included in the eigenvalues. As
shown in figure 2.2, the vortex center is classified as a repellingor attracting focus if the real parts are positive or negative,respectively. If the real part is zero, concentric ellipses occur
around the critical point.

2. Proposed method
2.1 Critical point extraction
The velocity vector data values are defined at vertices of theorthogonal grid in the ocean simulation result. In each gridcell, the velocity vector (ui, vi, wi) were given in each vertex Pi (i= 0-7) as shown in figure 2.1. Since the velocity vector isinterpolated inside the grid cell using tri-linear interpolation
function, the critical point can be determined by finding thelocation where the interpolated vector becomes(u, v, w) = (0, 0, 0).

Fig. 2.1 Vertices of the orthogonal grid.

Fig. 2.2 Classification of the critical point.
2.3 Estimation of the vortex domain
To understand the velocity field around the vortex center,
we often calculate a streamline whose starting point is locatednear the vortex center. In this case, the streamline is often
terminated using a criteria which defines a vortex domain. Weemploy a definition of the vortex domain proposed byPatrikalakis and et al[3]. According to the definition, thestreamline is calculated as follows:
1. Calculate a plane on which a vortex flow dominates bycalculating an eigenvector whose eigenvalue becomes real.
2. Calculate a streamline from a point which is located near
the vortex center and on the plane.
3. Project the streamline onto the plane in order to calculate
the incremental in the radius.
4. Terminate the streamline calculation if the incremental
exceeds a pre-determined value as shown in figure 2.3.

Fig. 2.3 Termination of the streamline
3. Experimental Setup
3.1 Velocity vector field

In the colormap of the sea surface temperature, the high andlow temperature values are continuously mapped to red and blue,
respectively. The spheres indicate the locations where CPUE
datasets were measured.
Figure 4.1 shows that the CPUE locations are distributednear the edges of two vortices, where the sea surface
temperatures are differently distributed. In the north or south
vortex, the temperature has the local minima or maxima. It is
well known that the Oyashio Current and the Kuroshio Current
collide in this domain and the collision facilitates the generationvortices. The CPUE locations indicates that the vortices play animportant role in the activation of the ocean food chainresources.
Figure 4.2 shows the temperature distribution on a verticalcross section which passes through the vortex center.

We used the velocity vector field included in the dataset
calculated by using MOVE (MRI Multivariate Ocean
Variational Estimation) System, which is an ocean data
assimilation system developed in Japan Meteorological Agency(JMA) / Meteorological Research Institute (MRI).
In this research, the region of interest is the offing ofAomori, western North Pacific. The 4DVAR version of MOVEsystem (MOVE-4DVAR) adopts, as the control variables (i.e.,the values optimized by the 4DVAR technique), a timespreading correction term instead of the initial value. Itsfeature includes time-spreading correction, consideringhorizontal correlation of the control variables and employing
vertical coupled corrections to temperature and salinity fields.
3.2 Fishery data of the neon flying squids
Datasets on the catch of the neon flying squids wereprovided by a test ship of the Aomori Prefectural Fisheries
Research Center. The datasets include the operation start dateand time and fishery position (latitude, longitude) watertemperature, the number of the fishing device, total capture
quantity, the operating hours, CPUE(Catch per unit effort),
which is expressed as follows:
CPUE = Cq / Fd / Oh(3.1)
Cq : capture quantity
Fd : the number of fishing device
Oh : operating hours
4. Results and Discussions
4.1 Relations with vortex and CPUE
Figure 4.1 shows a set of streamlines calculated from nearvortex centers in the MOVE dataset of February 13, 2002. The
sea surface temperature and CPUE locations are superimposed.

Fig.4.2 Vortex shape and seawater temperature distribution
The steep change in the temperature around the vortex
center may imply that there exists some vertical flow, that is an
upwelling current, which transports nutrient salts from thebottom of the sea to the near of the sea surface.
5. Conclusion
In this article, we figured out that vortex centers haverelation with CPUE locations where the Oyashio Current andthe Kuroshio Current collide. We identified the vortex centersby applying the critical point theory to the velocity fieldcalculated by the MOVE system.
In future, we will investigate the three-dimensional structure
which explains the way how the upwelling flow occurs near thevortex center by employing the velocity field defined on ahigher resolution grid which can express a subtle vortex, thescale of which ranges from a hundred meter to one kilometer.

References[1] Hideo Tameishi, relations with discovery and the saury first fishingof the season ground formation of the Sanriku coast minute vortex with
the PALSAR, photographic surveying and remote sensing, (2007), pp．
20-26．
[2] Helman J, Hesselink L, Representation and Display of Vector FieldTopologyin Fluid Flow Data Sets, Computer, (1989), pp．27-36．
[3] Guo D and Evangelinos C and Patrikalakis, Flow Feature Extraction
in Oceanographic Visualization, Computer Graphics International,(2004), pp.162-173．

Fig.4.1 February 13, 2002 CPUE and Vortices sea surface
temperature distribution