Indian Journal of Marine Sciences Vol. 33(4), December 2004, pp. 319-328

CBR spatial similarity analysis on mesoscale ocean eddies with remote sensing data

*Yunyan Du, Ce Li, Fenzhen Su, Tianyu Zhang & Xiaomei Yang

LREIS, Institute of Geographic Science and Natural Resources, CAS, Building 917, Datun Road Anwai Street, Beijing 100101, P.R. China

*[E-mail: duyy@lreis.ac.cn ] Received 30 December 2003, revised 25 October 2004

Ocean eddy Case-Based Reasoning (CBR) is developed and extended to the spatial-tempo domain in this paper to extract ocean eddy spatial similarity information in a quantificational manner, which can be very difficult to acquire using current routine eddy feature recognition and analysis algorithms. Present work includes three basic steps. First, information about the eddy’s spatial structure and attributes is obtained from the original remote sensing data. Then a library of historical eddy cases is built using the cases’ expression models. Finally, a Radius Vector Serial Analysis Model Based on Barycentre (RVSAMB) is provided to analyse the spatial similarity between the historical cases for further forecasting and dynamic analysis. In this study, a new quantitative method to analyse and extract ocean mesoscale eddy information using Case-based Reasoning is presented. Firstly, a historical ocean eddy case library was constructed based on the specific expression model. Then, the sketch of this method is discussed in detail, especially the similarity assessment method—“Radius Vector Serial Analysis Model Based on Barycentre”. Finally, a mesoscale warm eddy example in the Gulf Stream of the North Atlantic indicated that this is a feasible way to analyse ocean eddies.

[Key words: Mesoscale eddy, Case-Based Reasoning (CBR), Spatial similarity, Radius Vector Serial Analysis Model Based on Barycentre (RVSAMB)]

Introduction Over the past few decades, many studies have been made on the classification, distribution and spatial-temporal analysis of mesoscale eddies in the China Sea and West Pacific Ocean. A range of mathematic methods have been used to obtain a further understanding of mesoscale eddies. However, lack of high-resolution remote sensing data and the limitation of data assimilation and information fusion techniques have prevented the advance of time series analysis of mesoscale eddies in China. It is obvious that a new method needs to be established to utilize the current dataset to analyse time series of quantificational mesoscale eddies. Mesoscale eddies play a crucial role in the impact of the exchange of material and energy flux in the ocean and have attracted much attention from researchers. Su et al.1indirectly studied the eddies’ attributes and their development characteristics through water mass analysis research. Lu2 analysed the Kuroshio frontal eddy using a fuzzy multi-analysis technique. Tang et al.3 and Guo et al.4 reported the characteristics of the Kuroshio frontal eddy’s horizontal and vertical information by using

observation materials. Others have 5-8built a numerical model to analyse the characteristics and mechanisms of mesoscale eddies. The rapid development of remote sensing techniques has produced more and more multi-source and large-area ocean remote sensing data. How to retrieve the ocean eddy information from those remote sensing products and utilize them effectively in scientific applications has become an urgent priority. Meanwhile, recognising and retrieving ocean information using ocean knowledge based system and building a specific intelligent calculating model has also become a priority in international studies9. Since mesoscale eddies overlap on the average ocean current field, their occurrence follows laws with many phenomenal characteristics in ocean surface altitude, ocean water physical features and spatial morphology, which supply a solid base for recognizing and retrieving ocean eddy phenomena. However, eddies vary greatly in different local regions due to the levity of the ocean environment. For example, under the influence of shearing strength, the Kuroshio eddies at the turning point of the Chinese continental shelf become frontal eddies with a folding structure whose centre is in a

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long thin tape shape and the warm current develops into a warm filament structure. Such influence greatly reduces the efficiency and accuracy of the current quantitative method on eddies and obstructs the automatic quantitative retrieval and forecasting of eddy information. Case-based Reasoning (CBR)10-13, as an emerging branch of AI (artificial intelligence), has drawn great interest from AI experts who had been constrained with difficulties in knowledge extraction, manipulation, knowledge database construction, and maintenance connected with eddy research since the 1990’s. Studying Geo-Spatial complex systems has been regarded as a promising tool. CBR’s working mechanism is very similar to the logic of primitive human reasoning, which makes it a perfect model for human recognition. CBR is supposed to have the inborn ability of quantitative interpretation and prediction based simply on similarity of historical events, even when there is difficulty in getting the working mechanisms, principles, or building statistical models for those complex systems10. Methodology As mentioned above, the development of AI and the ocean features retrieving algorithm has provided a strong base technique for automatically retrieving eddy information. The CBR method doesn’t require understanding the mechanism of how a phenomenon develops, so it’s a simplified method, but with a high efficiency for solving very complicated problems. Although the mechanism of how ocean eddies are generated isn’t clearly understood yet, numerous

ocean eddy cases have been observed, analysed and studied. Viewed from this perspective, CBR is not only a fresh attempt for the extraction and quantificational forecasting of information on ocean eddies, but also an ideal approach to systematically studying ocean eddies. This paper tries to develop a new method, which is different with and better than current routine quantitative methods employed in ocean science in handling ocean eddy issues. Moreover, the typical history case library of ocean phenomena advocated by this method, will surely provide more material for any further study of ocean eddies. Framework of ocean eddy information extraction__The basic schedule of case reasoning is composed of four steps: retrieve, reuse, revise, and retain. The relatively complicated rule, presented by ocean eddies under the influence of ocean currents, seabed terrain, and relevant hydro-environment, belongs under the domain of geography to a certain extent. The basic framework of extraction of ocean eddy information is illustrated in Fig. 1. With the support of the GIS database and the ocean eddy case library, various rules of ocean eddies were studied and the structure of the case library was re-organized. Then similarity reasoning was applied to the cases to retrieve the information and to forecast eddies using the data. Presentation and organization of ocean eddy cases__The key item in building a case library is to present and organise ocean eddy cases with their volatile spatial pattern characteristics in a quantificational manner. Most current presentation

Fig. 1—Basic frame of ocean eddy information extraction using CBR

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Construction of a historical eddy case library __ The construction of a case library includes three steps shown as Fig. 2: data capture, case presentation, and case physical organization/storage. First, the attribute data and spatial data are encoded or digitalized from all kind of data sources such as remote sensing images, observation data, maps, publications and statistical data. Those data then are selected, sorted and re-encoded to form cases using the case presentation model mentioned above. Finally, the Geo-Database of ArcGIS, commercial production of ESRI Co., is redesigned to store ocean eddy cases. In this study, a Geo-Database is considered a case library.

models can be divided into four categories: conventional representation models14, structural representation models15, hierarchical representation models16, and Tesseral representation models17. However, none of these are suitable for describing the spatial information of an eddy. Studies of Jones & Roydhouse18 parameterised some of the spatial information and treated those spatial parameters as attributes with which to build cases. But this alternative solution is not a general approach to all of the problems and some important spatial information may even be lost. In order to extend the CBR method into the spatial-tempo domain, Du19 developed a comprehensive presentation model, which was successfully applied to China’s national high technique program (863 project)-Ocean Fishery Forecasting System. Present study adopts this presentation model, but with a much more advanced presentation of spatial information.

For a specific ocean eddy, the spatial information of the eddy is stored in a BLOB field while the other attribute information is stored in normal fields of the database and the ocean is identified by a unique case ID. Such a presentation model is not only favourable for obtaining for the eddy’s spatial morphology calculation and multi-eddy overlay analysis, but also very convenient to quickly extract needed cases with common database inquiry functions. The profile of the eddy can be obtained by using image enhancement by shape adaptation of scale-space operators using the automatic scale selection method20.The physical level of the eddy can be presented as a line feature and other eddy related attributes information, such as the position, time, intension and type, can all be stored in the ArcGIS Geo-Database.

The quantitative presentation model is made up of two parts: the attribute presentation model and the spatial presentation model. The attribute presentation model describes the attributes of an ocean eddy case, which includes: the name of the eddy, the time it occurs, the coordinates of the centre area, the type of eddy, its intensity, its duration, the life stage of the eddy, the ID of the eddy, the average temperature environment, and the salinity environment, etc. These attributes are properly encoded into numbers and the model organises them into an attributes eigenvector. The spatial presentation model employs some basic GIS features-point, multipoint, line, multi-line, polygon and region-to present the spatial morphology, or the pattern of the case. In this particular study, the morphology of an eddy is represented as an abstract line feature. With this information, we can write an eddy case symbolically as:

It is usually difficult to build a relatively complete historical eddy case library because of the data shortage and lack of information, especially for frontal eddies in certain sea regions. Two methods are used in the study to handle the problems of missing data/information- i) extract information of historical cases from remote sensing data, and ii) use similar information from the same type of eddies in nearby areas as a substitute. Both methods are discussed below.

Casei={Ai, Si}, i=1,2,…k; … (1)

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Similar reasoning model of ocean eddy cases__ After the case library is built, we try to find historical cases that are similar to a new eddy case. Then the information on how they occurred and developed is used to forecast the next developmental stage of the new case. The key technique in ocean eddy information recognition, extraction, and forecasting is the CBR similarity model. Figure 3 illustrates the reasoning flow in detail. The whole reasoning process is mainly comprised of three steps: extracting similar

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Indian Journal of Marine Sciences Vol. 33(4), December 2004, pp. 319-328

Fig. 2—Flow chart of case library construction

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Fig. 3—Flow chart of ocean eddy similarity reasoning

historical cases in attribute domains, assessing spatial similarity, and forecasting the current eddies.

(1) Extracting similar historical ocean eddy cases based on attributes -In this step, we should decide whether a pair of given cases are similar and how similar they are only according to their attributes and choose similar historical cases for further analysis. Here, a Euclidean distance is measured for each pair of cases to determine the degree of similarity in the attribute domain as:

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where, Ai is the attribute eigenvector of Case i, wk is the weight coefficient of the element k in the character vector, which is pre-determined by expert experience. According to experimental knowledge, a threshold is set to test whether a pair of cases is similar or not. If the similarity calculated as Eq. (1) is greater than the threshold, the pair is treated similar; otherwise, the pair is not similar. Obviously, all the character-matched cases of a given case are inside a hyper-ellipsoid in character dimensions. To pick out all similar historical cases of a given new case, we have to calculate all similarities between every historical case and the new one, which can be a time-consuming process for a large case library. A filter window, a

hyper cube in character dimensions, is applied to extract those character-matched cases instead to promote the efficiency in this practical application. The window is given as:

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Fig. 4—Demonstration of a barycenter calculation for any curve in space

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where, xi is the element i of the character vector of the new case; wi is the weight coefficient of the element i in the character vector. All cases that fall in the filter window are obtained as candidate similar cases of the new case. They will then be further examined by the spatial similarity assessment. (2) Assessing spatial similarity - Many reports21-24 on ocean eddy have shown that the inner physical mechanism determines the morphology of the eddy, which means similar eddies share similar morphology and also implies eddies that have similar morphology have a similar inner physical mechanism. Here an algorithm, with properties of shift invariance, rotation invariance and linear transformation invariance, is introduced to describe the degree of similarity of appearance in two different eddies. As shown in section of “Presentation and organization of ocean eddy cases”, the morphology or the spatial information of each eddy case are presented as linear objects. Thus, for present study, describing the spatial similarity between two eddies is equivalent to evaluating the similarity between two outlines of those eddies. Radius Vector Serial Analysis Model Based on Barycentre (RVSAMB) has been developed to evaluate the degree of spatial similarity of linear objects. The central aim of RVSAMB is to generate a formatted eigenvector, which describes the main geometric property of a line. For each line, the similarities of the eigenvector of each pair of lines are then calculated using12 a statistical approach. The algorithm in detail is given as below: Given a line l with n vertices: {(x1,y1), (x2,y2),…, (xn,yn)}, as shown in Fig. 4, and supposing the mass density along the line is uniform, the barycentre (x*,y*) of l is:

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So far, we can assess the spatial similarity of a pair of eddies at the correlation coefficient (rij) of their radius vector series. As a final step, we also set an empirical constant as a spatial similarity threshold to extract similar cases from those candidate similar cases we obtained in step one. (3) Extracting and forecasting ocean eddy information -- The cases that pass both attribute and spatial similarity tests are considered similar cases and will be used to predict the trend of the new case’s development. The prediction of the status of the new case after a time period, t, is based on the average trend in both attribute and spatial domains that those similar cases underwent during the same time period, t. A brief outline of the prediction model is given below. First, object cases for each similar case are retrieved from the case library, which match the status of similar cases after the time duration, t. Then differences, including the morphology variation in the spatial domain and the value displacement in the

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attribute domain, are analysed for each pair of object cases and similar cases during the time period, t. An average difference, or so-called trend is calculated with the weighted average algorithm. Finally, this average difference, which contains spatial and attribute information, is added to the new case. The result is the estimation of the status of the new case after a time period, t. Application demonstration To verify the validity of present model and algorithm, a simple analysis on the dynamic development and spatial similarity of a typical mesoscale warm eddy in the Gulf Stream of the North Atlantic is presented. In this example, we selected three Coastal Zone Colour Scanner (CZCS) pigment images taken on May 2nd, 1979, May 3rd, 1979, May 8th, 197925, and one MODIS SST image taken on May 6th, 2004 respectively as historical cases (Fig. 5). A CZCS pigment image taken on May 7th, 1979 was

also selected as the new case (Fig.5.5). The first four images share a briefly similar spatial pattern: manifest north of the Gulf Stream, they meander in the slope water, just downstream of Cape Hatteras, which is highlighted with orange arrow lines; and a large warm core ring in further east, which is highlighted with white lines. Whereas, the last image has a very different spatial pattern, only with a cold core ring in further east, which is highlighted with white line. After digitalizing outlines of these five eddies, the GIS analysis was employed to measure the geo-location of central points and diameters of the warm-core rings, shown as Table 1. Then according to the presentation model mentioned earlier, we created five cases corresponding to these five images and the other relevant data. A mini case library containing four historical cases was then built. We skipped the attribute similarity test to focus on the spatial similarity analysis. For these cases, Radius

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Vector Series with a size 100 were generated to describe the spatial morphology (Fig. 6). Figure 6 A shows the outline, barycentre, n equi-part points and centrobaric radius vectors of each individual ocean eddy case. According to Eq. (6) in section 2.4, spatial similarity coefficients of each pair of cases were

calculated (Fig. 6 B). The result is given in Table 2, which shows that the target case was most similar with the historical case 3 in morphology view. This result corresponds to our analysis in attribute domain.

Table 1—Geo-location and radius of each case

Case 1 Case 2 Case 3 New Case * Case 5

Location 68.75ºW, 38.7ºN 68.77ºW, 38.97ºN 68.99ºW, 39.06ºN 68.98ºW, 38.95ºN 69.2ºW, 39.03ºN

Diameter 89.02km 88.5km 102.6km 92.11km 39.9km

Table 2—Spatial similarity coefficients of history ocean eddy cases

Similarity coefficients Case (1) Case (2) Case (3) New Case Case (5)

Case (1) 1.0000 0.9611 0.5709 0.5372 0.5421 Case (2) 0.9611 1.0000 0.4249 0.3769 0.5196 Case (3) 0.5709 0.4249 1.0000 0.8732 0.3110 New Case 0.5372 0.3769 0.8732 1.0000 0.5949 Case ( 0.5421 0.5196 0.3110 0.5949 1.0000

Fig. 5—Illustration of some historical ocean eddy cases and the target case 1) case on 2th May 1979, 2) case on 3th May 1979, 3) case on 8th May 1979, 4) given case, 5) case on 6th May 2004

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Fig. 6—Illustration of ocean eddy recognition and forecasting by CBR, A) spatial similar analysis of the five cases,

B) distance series of centrobaric radius vectors

If the other attribute data can be obtained in detail, then the related information of the current ocean eddy (the new case) can be forecasted and analyzed in a quantificational manner. In the Krushio stream off the East China Sea, the same method can be used to forecast the development of eddies. But no exact example can be given at this moment due to the lack of historical ocean eddy cases. It will be tested in future studies. Discussion Compared with CBR methods, which treat spatial information as parameters, abstracting an eddy’s spatial information as a simple geometric element (the so-called “sketch” model) has the advantage of describing the morphology elaborately. A “sketch” model can discriminate the subtle distortion between different shapes and the RVSAMB model can further measure the similarity of two shapes. According to the demonstration, the present results are reasonable and satisfying. Although in this study the line feature is employed to sketch an eddy, many different geometric models, which are universally used in Geographical Information System (GIS), can be used to present the morphology of an eddy: multi-point, multi-line, polygon, and their combinations. The selection of a specific geometric model to present the spatial information of a case depends on the character of the case of the studying, the available data source, and the reasoning model that will be applied in the sequel. As for our demonstration, the reason for using a single line to present the spatial information of an eddy is that the most distinct geometric character of mesoscale eddies in CZCS images is a thin wrapped bright tape curling around the warm/cold core. Obviously, the geometric model for this study was decided upon more or less by instinct. The optimum selection of the sketch geometric model needs further study. Besides the design of the case presentation model, the similarity model and the reasoning model, the information extraction accuracy of the CBR greatly depends on the volume of the historical eddy case library and whether those historical cases are representative of eddies in the whole study area. With further advances in remote sensing technology, multi-temporal, multi-band, and multi-dimension data will

become more and more handy, which will enhance the construction of typical historical case libraries. The level of quantification and the accuracy of this method can be greatly improved in future. Meanwhile this research establishes the conditions for further studies of ocean dynamics. Acknowledgement This study was fully supported by the National 863 High Technology Programs of China (Project No. 2002AA639640 and 2001AA633010). The authors would like to sincerely thank the ocean coast research group for providing advice on the algorithms of similarity reasoning, and gratitude to Prof. Liu Baoying (First institute of oceanography, State Oceanic Administration) for providing knowledge and data on ocean eddies. References

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