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Chin. Phys. B, 2020, Vol. 29(10): 108901    DOI: 10.1088/1674-1056/aba27d

Modeling and analysis of the ocean dynamic with Gaussian complex network

Xin Sun(孙鑫)1, Yongbo Yu(于勇波)1, Yuting Yang(杨玉婷)1, Junyu Dong(董军宇)1,2,†(), Christian Böhm(陈学恩)3, Xueen Chen4
1 Department of Computer Science and Technology, Ocean University of China, Qingdao 266000, China
2 Frontiers Science Center for Deep Ocean Multispheres and Earth System, Qingdao 266000, China
3 Institut für Informatik, Ludwig Maximilian University of Munich, Munich 80331-81929, Germany
4 College of Physical and Environmental Oceanography, Ocean University of China, Qingdao 266000, China

The techniques for oceanographic observation have made great progress in both space-time coverage and quality, which make the observation data present some characteristics of big data. We explore the essence of global ocean dynamic via constructing a complex network with regard to sea surface temperature. The global ocean is divided into discrete regions to represent the nodes of the network. To understand the ocean dynamic behavior, we introduce the Gaussian mixture models to describe the nodes as limit-cycle oscillators. The interacting dynamical oscillators form the complex network that simulates the ocean as a stochastic system. Gaussian probability matching is suggested to measure the behavior similarity of regions. Complex network statistical characteristics of the network are analyzed in terms of degree distribution, clustering coefficient and betweenness. Experimental results show a pronounced sensitivity of network characteristics to the climatic anomaly in the oceanic circulation. Particularly, the betweenness reveals the main pathways to transfer thermal energy of El Niño–Southern oscillation. Our works provide new insights into the physical processes of ocean dynamic, as well as climate changes and ocean anomalies.

Keywords:  complex networks      ocean dynamic      Gaussian mixture model      physical processes  
Received:  17 April 2020      Revised:  19 June 2020      Published:  05 October 2020
PACS:  89.75.Fb (Structures and organization in complex systems)  
  05.45.Tp (Time series analysis) (Networks)  
Corresponding Authors:  Corresponding author. E-mail:   
About author: 
†Corresponding author. E-mail:
* Project supported by the National Natural Science Foundation of China (Grant Nos. U1706218, 61971388, and L1824025).

Cite this article: 

Xin Sun(孙鑫), Yongbo Yu(于勇波), Yuting Yang(杨玉婷), Junyu Dong(董军宇), Christian Böhm(陈学恩), Xueen Chen Modeling and analysis of the ocean dynamic with Gaussian complex network 2020 Chin. Phys. B 29 108901

Fig. 1.  

Process of complex network modeling based on surface sea temperature (SST).

Fig. 2.  

Degree distribution of nodes in (left) SG-network (right) MG-network.

Fig. 3.  

Degree logD distributions with geographic locations in the global ocean: (a) SG-network, (b) MG-network.

Fig. 4.  

Degree distributions in the northern hemisphere.

Fig. 5.  

Clustering coefficient distribution of the network model at geographic location.

Fig. 6.  

Betweenness distribution of the network model at geographic location.

Fig. 7.  

Scatter plots of betweenness against degree of SG-network

Clustering coefficient Distance Diameter
La Niña period MG-network 0.136 2.083 4
SG-network 0.102 2.905 8
Normal period MG-network 0.302 1.98 3
SG-network 0.132 2.07 4
El Niño period} MG-network 0.1585 8189 6
SG-network 0.261 1.809 4
Table 1.  

Average clustering coefficient, distance and diameter for the networks constructed by Gaussian approach in three periods.

Zhang L, Huang S X, Shen C, Shi W L 2011 Chin. Phys. B 20 129201 DOI: 10.1088/1674-1056/20/12/129201
Shen X Y, Qing T, Li X F 2013 Chin. Phys. B 22 94213 DOI: 10.1088/1674-1056/22/9/094213
Chave A D, Arrott M, Farcas C, Farcas E, Krueger I, Meisinger M, Orcutt J A, Vernon F L, Peach C, and S Oscar Oceans May 11–14, 2009 Bremen, Germany 1
Liu Y j, Qiu M, Liu C, Guo Z W 2017 Pers. Ubiquitous Comput. 21 55 DOI: 10.1007/s00779-016-0980-2
Owens D, Best M, Guillemot E, Jenkyns R Oceans B 2010 May 24–27 2010 Sydney, Australia 1
Sun X, Chen C, Dong J, Liu D, Hu G 2020 Knowl.-Based Syst. 196 105824 DOI: 10.1016/j.knosys.2020.105824
Pradhan R, Aygun R S, Maskey M, Ramachandran R, Cecil D J 2017 IEEE Trans. Image Process. 27 692 DOI: 10.1109/TIP.2017.2766358
Havlin S, Kenett D Y, Jacob E B, Bunde A, Cohen R 2012 Eur. Phys. J. Spec. Top. 214 273 DOI: 10.1140/epjst/e2012-01695-x
Wu Y, Shang Y, Chen M et al. 2008 IEEE Trans. Circuits Syst. 214 1335 DOI: 10.1063/1.2939136
Tominski C, Donges J F, Nocke T 2011 15th International Conference on Information Visualisation July 13–15, 2011 London, UK 298 305 DOI: 10.1109/IV.2011.12
Donges J F, Zou Y, Marwan N, Kurths J 2009 Eur. Phys. J. Spec. Top. 174 157 DOI: 10.1140/epjst/e2009-01098-2
Charakopoulos A K, Katsouli G A, Karakasidis T E 2009 Physica A 495 436 DOI: 10.1016/j.physa.2017.12.027
Sun X, Song Z, Dong J, Yu Y, Plant C, Böhm C 2019 Thirty-Third AAAI Conference on Artificial Intelligence January 29–31, 2019 Hawaii, USA 5041 5048 DOI: 10.1609/aaai.v33i01.33015041
Steinhaeuser K, Chawla N V, Ganguly A R 2009 Proceedings of the Third International Workshop on Knowledge Discovery from Sensor Data June 28, 2009 Paris, France 23 31 DOI: 10.1145/1882471.1882476
Donges J F, Petrova I, Loew A, Marwan N, Kurths J 2015 Clim. Dynamics 45 2407 DOI: 10.1007/s00382-015-2479-3
Meng J, Fan J F, Ashkenazy Y, Havlin S 2017 Chaos: An Interdisciplinary J. Nonlinear Sci. 27 035807 DOI: 10.1063/1.4975766
Donges J F, Zou Y, Marwan N, Kurths J 2009 Eur. Phys. J. Special Topics 174 157 DOI: 10.1140/epjst/e2009-01098-2
Boers N, Bookhagen B, Marwan N, Kurths J, Marengo J 2013 Geophys. Res. Lett. 40 4386 DOI: 10.1002/grl.50681
Boers N, Bookhagen B, Barbosa H M J, Marwan N, Kurths J, Marengo J A 2014 Nat. Commun. 5 5199 DOI: 10.1038/ncomms6199
Josef L, Avi G, Mikhail I B, Armin B, Shlomo H, Hans J S 2014 Proc. Natl. Acad. Sci. USA 111 2064 DOI: 10.1073/pnas.1323058111
Tsonis A A, Swanson K L, Wang G 2008 J. Clim. 21 2990 DOI: 10.1175/2007JCLI1907.1
Tsonis A A, Roebber P J 2004 Phys. A: Stat. Mech. Its Appl. 333 497 DOI: 10.1016/j.physa.2003.10.045
Yamasaki K, Gozolchiani A, Havlin S 2008 Phys. Review Letters 100 228501 DOI: 10.1103/PhysRevLett.100.228501
Tsonis A A, Swanson K L 2008 Phys. Rev. Lett. 100 228502 DOI: 10.1103/PhysRevLett.100.228502
Iglesias G, Kale D C, Liu Y 2015 The 5th International Workshop on Climate Informatics September 24–25, 2015 Boulder, USA
Fan J F, J M, Chen X S, Ashkenazy Y, Havlin S 2016 Sci. Chin. Phys. Mech. Astron. 60 010531 DOI: 10.1007/s11433-016-0362-2
Ford J D, Tilleard S E, Lea B F, Araos M, Biesbroek R, Lesnikowski A C, MacDonald G K, Hsu A, Chen C, Bizikova L 2016 Proc. Natl. Acad. Sci. USA 113 10729 DOI: 10.1073/pnas.1614023113
Wang Y H, Shen X R, Yang S Q, Gao Z K 2020 Europhys. Lett. 128 60005 DOI: 10.1209/0295-5075/128/60005
Feng Q Y, Henk A D 2017 Chaos: An Interdisciplinary J. Nonlinear Sci. 27 035801 DOI: 10.1063/1.4971784
Wiedermann M, Radebach A, Donges J F, Kurths J, Donner R V 2016 Geophys. Res. Lett. 43 7176 DOI: 10.1002/2016GL069119
Tsonis A A, Swanson K L, Roebber P J 2006 Bull. Am. Meteorological Soc. 87 585 DOI: 10.1175/BAMS-87-5-585
Zerenner T, Friederichs P, Lehnertz K, Hense A 2014 Chaos: An Interdisciplinary J. Nonlinear Sci. 24 023103 DOI: 10.1063/1.4870402
Zhe J, Li X F, Zhou Y S, Gao S T 2012 Chin. Phys. B 21 054215 DOI: 10.1088/1674-1056/21/5/054215
Smith N R 2000 Adv. Space Res. 25 1089 DOI: 10.1016/S0273-1177(99)00868-6
Bohm C, Pryakhin A, Schubert M 2006 Proceedings of the 22nd International Conference on Data Engineering April 3–7, 2006 Atlanta, GA, USA 9 DOI: 10.1109/ICDE.2006.159
Freeman L C 1978 Soc. Netw. 1 215 DOI: 10.1016/0378-8733(78)90021-7
Duncan O D 1968 Am. Sociological Rev. 33 457 DOI: 10.2307/2091921
Huang J P, Kaz H, Amir S 1998 Geophys. Res. Lett. 25 2707 DOI: 10.1029/98GL01936
Fronczak A, Fronczak P, Hołyst J A 2007 Phys. Rev. E 76 061106 DOI: 10.1103/PhysRevE.76.061106
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[2] Luo Ying, Ma Ben-Kun, Duan Su-Qing, Zhao Xian-Geng, Wang Li-Min. Effects of a donor on the bond property of quantum-dot molecules[J]. Chin. Phys., 2004, 13(6): 942 -947 .
[3] Yu Hua-Ling, Wang Zhi-Guo, Peng Ju. Phase coherence of the electron and hole in a ferromagnetic film in proximity with a superconductor[J]. Chin. Phys. B, 2008, 17(12): 4627 -4634 .
[4] Zheng You-Jin, Li Yan-Tao, Zhou Lin, Jia Xiao-Peng, Ma Hong-An. Synthesis of industrial diamonds using FeNi alloy powder as catalyst[J]. Chin. Phys. B, 2008, 17(12): 4665 -4668 .
[5] He Ji-Fang, Niu Zhi-Chuan, Chang Xiu-Ying, Ni Hai-Qiao, Zhu Yan, Li Mi-Feng, Shang Xiang-Jun. Molecular beam epitaxy growth of GaAs on an offcut Ge substrate[J]. Chin. Phys. B, 2011, 20(1): 18102 -018102 .
[6] Lin Fang, Bao Jing-Dong. Environment-dependent continuous time random walk[J]. Chin. Phys. B, 2011, 20(4): 40502 -040502 .
[7] Li Chun-Yan, Wang Jiang-Bin, Wang Yi-Qian. Microstructure and photocatalytic activity of titanium dioxide nanoparticles[J]. Chin. Phys. B, 2012, 21(9): 98102 -098102 .
[8] Hong You-Li, Zhang Kai, Wang Zhi-Li, Zhu Zhong-Zhu, Zhao Xue-Jiao, Huang Wan-Xia, Yuan Qing-Xi, Zhu Pei-Ping, Wu Zi-Yu. Reconstructing a complex field from a series of its near-field diffraction patterns[J]. Chin. Phys. B, 2012, 21(10): 104202 .
[9] Niu Peng-Bin, Wang Qiang, Nie Yi-Hang. Transport through artificial single-molecule magnets: Spin-pair state sequential tunneling and Kondo effects[J]. Chin. Phys. B, 2013, 22(2): 27307 -027307 .
[10] Lai Ling-Ling, Cheng Rong-Jun, Li Zhi-Peng, Ge Hong-Xia. The KdV-Burgers equation in modified speed gradient continuum model[J]. Chin. Phys. B, 2013, 22(6): 60511 -060511 .