Visualization for Ocean General Circulation Model via
Multi-dimensional Transfer Function and Multivariate Analysis
Daisuke Matsuoka 1, Fumiaki Araki 1, Shinichiro Kida 1, Hideharu Sasaki 1, and Bunmei Taguchi 1
11

Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Japan

Introduction

With advances in supercomputing technology, ultra-highresolution large-scale simulation study has been the mainstream
in the field of ocean science. The dataset from such simulation is
not only large in size, but also contains a lot of useful
information. However, as the geophysical fluid simulation, it isdifficult to understand such information hiding in the dataset
due to the complexity of ocean dynamics and the number ofphysical variables. In order to obtain scientific knowledge fromlarge-scale simulation data, it is important to effectively extract
and to efficiently express the characteristic feature [1, 2].
The aim of this study is how to solve the above problem. In
this study, a multi-dimensional transfer function to emphasis thefeature such as ocean currents and vortices from OFES (Oceangeneral circulation model for the Earth Simulator) [3, 4] dataset
is proposed. Furthermore, a multivariate analysis to extract suchfeatures is developed. This paper describes the experimental
results of the applying the multi-dimensional transfer function
and multivariate analysis to the visualization of Oceanic Global
Circulation Model data.
2

Feature Emphasise Visualization
dimensional Transfer Function

via

(a)

(b)

Multi-Visualization of simulation results is effective way tounderstand a complex phenomenon and configuration intuitively.
However, representation using a conventional transfer function
mapping from one scalar value to one color and opacity is notgood enough to understand its fine structure. For example, Fig.1.
(a) shows the visualization result of Sea Surface Temperature(SST) distribution calculated by the OFES with horizontal
resolution of 1/10 degree via the traditional transfer function ofa rainbow color map. The color red indicates high value, blue is
low as shown color bar in the bottom right of the figure. Fig.1.
(b) shows the magnitude of sea surface velocity. The counter
color in the red and black area denotes high and slow speed,respectively. In such a general color map, it is suitable forseeing the distribution of the value. However, it is not easy torepresent the difference of flow speeds in the same temperature
region.
In this study, a multivariate color map which not only
assigns Hue (H) to one value but also assigns Saturation (S) andBrightness (V) to other variables is proposed in order torepresentation not only one value but also two or more values.
In Fig.1.(c), rainbow colors represent the SST and brightness
represents the flow speed (the bright color indicates fast flow,
and the dark color indicates slow flow). The temperature and theflow speed can be recognized simultaneously by assigning twovariables to H and B. The flow speed range from 0.0 m/s to 1.0m/s corresponds to the range of V from 0.5 to 1.0. Fig.1. (c)effectively emphasis the heat transfer by the ocean currents andvortices than Fig.1. (a) and (b). For instance, the Kuroshio,
North Pacific Current, Agulhas current and Antarctic
Circumpolar Current and its heat transfer can be seen in thisfigure.

(c)Fig. 1. The distribution of (a) Sea Surface Temperature(SST), (b) magnitude velocity and (c) mixed image of (a)and (b) via multi-dimensional transfer function.
3

Feature Extraction and Visualization via Cluster
Analysis

In order to accuracy set a transfer function using three ormore variables, it is necessary to extract characteristic featuresusing semi-automatic objective analysis. In this section, cluster
analysis which is one of multivariate analysis techniques is
improved and applied to extract ocean currents.
3.1

Application of Density-based Cluster Analysis
Cluster analysis is the task of assigning a set of objects into
groups called cluster so that the objects in the same cluster are
more similar to each other than to those in other clusters.
Several cluster analysis approaches have been proposed. They
may be divided into following 3 types: Hierarchical method,
Non-hierarchical method (k-means) and Density-based method[5].

The point about the feature of ocean currents is that twoelements (data) in a same current are not always similar but
continuity. Hence, we choose density-based method [6] whichuses the connectivity and density in variable space. In thisresearch, we originally improved this cluster analysis method
and applied it to extraction of ocean currents. In the our method,
it is necessary to set the following parameters, a position of
initial seed, density in the variable space, range for calculating
density, range for exploration and range for clustering. Initialseeds and clustering results is shown in Fig.2. The red and blue
area indicates the Kuroshio and Oyashio, respectively. Bothresults can be seen that the clustering is roughly correct.

(a)

(b)

Fig. 2. Clustering result of Oyashio and Kuroshio using
density based method.
Application of Non-Hierarchical and HierarchicalHybrid Cluster Analysis
Although the density-based method can extract ocean
currents, its computational cost is too high. In this study, weadopted a non-hierarchical cluster method in which thecomputational complexity and the memory size are notrestricted.
Non-hierarchical algorithms [7] divide a set of elements intok partitions or groups with each partition representing a cluster.
k initial cluster centroids are selected manually using domain
knowledge. In clustering analysis, one of the important steps isto select a distance measure, which can determine how thesimilarity of two elements is calculated. The distance between
two elements (i and j) in 4-dimensional Euclidean space isdefined as:
D2 ij = CT (Ti – Tj)2 + CV (Vi – Vj)2 + CX (Xi – Xj)2 + CY (Yi – Yj)2
where, T, V, X and Y is temperature, flow speed, x-position, yposition, respectively, and CT, CV, CX, and CY are constantnumber to make dimensionless quantity of similarity.
The resulting image of non-hierarchical cluster analysis and16 centroids are shown in Fig.2. (a). In order to visualize theresult, each cluster is indicated by a different color. Not only theKuroshio (cluster #1 and #2), the Kuroshio Extension region(cluster #3 and #4) and the Oyashio (cluster #14 and #15) but
also the mixed layer in the Kuroshio/Oyashio Extension region
and the vortices in the Sea of Japan are clustering almost
correctly.
Hierarchical algorithm is a method of cluster analysis whichseeks a hierarchy of clusters or elements. Next, hierarchicalmethod is adopted to extract the hierarchical structure of thesmall clusters obtained by the non-hierarchical method. The
hierarchical structures using the hierarchical method isrepresented as a tree diagram called dendrogram as shown in
Fig.3. (b). We can recognize from Fig.3. (b) that Kuroshio andOyashio is composed from cluster #1 - #4 and cluster #14 and#15, respectively.

Fig. 3. Clustering results of Oyashio and Kuroshio using(a) non-hierarchical method and (b) hierarchical method.

3.24Conclusion

This paper described a new multi-dimensional transfer
function that can emphasis the ocean currents and multivariate
analysis methods that can extract the ocean currents. These
results lead to the conclusion that multi-dimensional transfer
function and multivariate analysis are effective method in order
to visualize and understand high resolution simulation data. In
the visualization for next generation simulation, it is necessary
to efficiently extract useful information hiding into the datasetsand to effectively express such information.
Acknowledgements
This work was supported by KAKENHI (24650045) for Grantin-Aid for Challenging Exploratory Research.
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