Cite this paper:
YUAN Shijin, LI Mi, WANG Qiang, ZHANG Kun, ZHANG Huazhen, MU Bin. Optimal precursors of double-gyre regime transitions with an adjoint-free method[J]. HaiyangYuHuZhao, 2019, 37(4): 1137-1153

Optimal precursors of double-gyre regime transitions with an adjoint-free method

YUAN Shijin1, LI Mi1, WANG Qiang2, ZHANG Kun2, ZHANG Huazhen1, MU Bin1
1 School of Software Engineering, Tongji University, Shanghai 201804, China;
2 Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
In this paper, we find the optimal precursors which can cause double-gyre regime transitions based on conditional nonlinear optimal perturbation (CNOP) method with Regional Ocean Modeling System (ROMS). Firstly, we simulate the multiple-equilibria regimes of double-gyre circulation under different viscosity coefficient and obtain the bifurcation diagram, then choose two equilibrium states (called jet-up state and jet-down state) as reference states respectively, propose Principal Component Analysis-based Simulated Annealing (PCASA) algorithm to solve CNOP-type initial perturbations which can induce double-gyre regime transitions between jet-up state and jet-down state. PCASA algorithm is an adjoint-free method which searches optimal solution randomly in the whole solution space. In addition, we investigate CNOP-type initial perturbations how to evolve with time. The results show:(1) the CNOP-type perturbations present a two-cell structure, and gradually evolves into a three-cell structure at predictive time; (2) by superimposing CNOP-type perturbations on the jet-up state and integrating ROMS, double-gyre circulation transfers from jet-up state to jet-down state, and vice versa, and random initial perturbations don't cause the transitions, which means CNOP-type perturbations are the optimal precursors of double-gyre regime transitions; (3) by analyzing the transition process of double-gyre regime transitions, we find that CNOP-type initial perturbations obtain energy from the background state through both barotropic and baroclinic instabilities, and barotropic instability contributes more significantly to the fast-growth of the perturbations. The optimal precursors and the dynamic mechanism of double-gyre regime transitions revealed in this paper have an important significance to enhance the predictability of double-gyre circulation.
Key words:    optimal precursors|double-gyre regime transitions|conditional nonlinear optimal perturbation (CNOP)|Principal Component Analysis-based Simulated Annealing (PCASA)|multipleequilibria regimes   
Received: 2017-12-17   Revised: 2018-02-12
PDF (6701 KB) Free
Print this page
Add to favorites
Email this article to others
Articles by YUAN Shijin
Articles by LI Mi
Articles by WANG Qiang
Articles by ZHANG Kun
Articles by ZHANG Huazhen
Articles by MU Bin
Budgell W P. 2005. Numerical simulation of ice-ocean variability in the Barents Sea region. Ocean Dynamics, 55(3-4):370-387.
Chang Y L, Oey L Y. 2014. Analysis of STCC eddies using the Okubo-Weiss parameter on model and satellite data.Ocean Dynamics, 64(2):259-271.
Di Lorenzo E. 2003. Seasonal dynamics of the surface circulation in the Southern California current system.Deep Sea Research Part Ⅱ:Topical Studies in Oceanography, 50(14-16):2 371-2 388.
Dijkstra H A. 2005. Nonlinear Physical Oceanography:A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Nino. Springer Science & Business Media, New York.
Dinniman M S, Klinck J M, Jr W O S. 2003. Cross-shelf exchange in a model of the Ross Sea circulation and biogeochemistry. Deep-Sea Research Part Ⅱ, 50(22):3 103-3 120.
Duan W S, Mu M, Wang B. 2004. Conditional nonlinear optimal perturbations as the optimal precursors for El Nino-Southern Oscillation events. Journal of Geophysical Research:Atmospheres, 109(D23):D23105.
Feng M, Meyers G. 2003. Interannual variability in the tropical Indian Ocean:a two-year time-scale of Indian Ocean Dipole. Deep Sea Research Part Ⅱ:Topical Studies in Oceanography, 50(12-13):2 263-2 284.
Haidvogel D B, Arango H G, Hedstrom K, Beckmann A, Malanotte-Rizzoli P, Shchepetkin A F. 2000. Model evaluation experiments in the North Atlantic Basin:simulations in nonlinear terrain-following coordinates.Dynamics of Atmospheres and Oceans, 32(3-4):239-281.
Hill C, DeLuca C, Balaji, Suarez M, Da Silva A. 2004. The architecture of the Earth System modeling framework.Computing in Science & Engineering, 6(1):18-28.
Jiang S, Jin F F, Ghil M. 1995. Multiple equilibria, periodic, and aperiodic solutions in a wind-driven, double-gyre, shallow-water model. Journal of Physical Oceanography, 25(5):764-786.
Liu Y M. 2008. Maximum principle of conditional optimal nonlinear perturbation. Journal-East China Normal University (Natural Science), (2):131-134. (in Chinese with English abstract)
Mahadevan A, Lu J, Meacham S, Malanotte-Rizzoli P. 2001.The predictability of large-scale wind-driven flows.Nonlinear Processes in Geophysics, 8(6):449-465.
Marchesiello P, Mcwilliams J C, Shchepetkin A. 2003.Equilibrium structure and dynamics of the California current system. Journal of Physical Oceanography, 33(4):753-783.
Moore A M, Arango H G, Di Lorenzo E, Di Cornuelle B, Miller A J, Neilson D J. 2004. A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modelling, 7(1-2):227-258.
Moore A M. 1999. Wind-induced variability of ocean gyres.Dynamics of Atmospheres and Oceans, 29(2-4):335-364.
Mu B, Wen S C, Yuan S J, Li H Y. 2015. PPSO:PCA based particle swarm optimization for solving conditional nonlinear optimal perturbation. Computers & Geosciences, 83:65-71.
Mu M, Duan W S, Wang B. 2003. Conditional nonlinear optimal perturbation and its applications. Nonlinear Processes in Geophysics, 10(6):493-501.
Mu M, Duan W S, Wang J C. 2002. The predictability problems in numerical weather and climate prediction. Advances in Atmospheric Sciences, 19(2):191-204.
Mu M, Sun L, Dijkstra H A. 2004. The sensitivity and stability of the ocean's thermohaline circulation to finite-amplitude perturbations. Journal of Physical Oceanography, 34(10):2 305.
Mu M, Yu Y S, Xu H, Gong T T. 2014. Similarities between optimal precursors for ENSO events and optimally growing initial errors in El Niño predictions. Theoretical and Applied Climatology, 115(3-4):461-469.
Nauw J J, Dijkstra H A, Chassignet E P. 2004. Frictionally induced asymmetries in wind-driven flows. Journal of Physical Oceanography, 34(9):2 057-2 072.
Nauw J J, Dijkstra H A. 2001. The origin of low-frequency variability of double-gyre wind-driven flows. Journal of Marine Research, 59(4):567-597.
Oey L Y. 2008. Loop Current and deep eddies. Journal of Physical Oceanography, 38(7):1 426-1 449.
Peliz A, Dubert J, Haidvogel D B et al. 2003. Generation and unstable evolution of a density-driven Eastern Poleward Current:The Iberian Poleward Current. Journal of Geophysical Research Oceans, 108(C8):3 268.
Pierini S. 2006. A kuroshio extension system model study:decadal chaotic self-sustained oscillations. Journal of Physical Oceanography, 36(8):1 605-1 625.
Pierini S. 2010. Coherence resonance in a double-gyre model of the Kuroshio Extension. Journal of Physical Oceanography, 40(1):238-248.
Primeau F, Newman D. 2008. Elongation and contraction of the western boundary current extension in a shallowwater model:a bifurcation analysis. Journal of Physical Oceanography, 38(7):1 469-1 485.
Primeau F. 2002. Multiple equilibria and low-frequency variability of the wind-driven ocean circulation. Journal of Physical Oceanography, 32(8):2 236-2 256.
Qin X H, Duan W S, Mu M. 2013. Conditions under which CNOP sensitivity is valid for tropical cyclone adaptive observations. Quarterly Journal of the Royal Meteorological Society, 139(675):1 544-1 554.
Qin X H, Mu M. 2011. A study on the reduction of forecast error variance by three adaptive observation approaches for tropical cyclone prediction. Monthly Weather Review, 139(7):2 218-2 232.
Sapsis T P, Dijkstra H A. 2013. Interaction of additive noise and nonlinear dynamics in the double-gyre wind-driven ocean circulation. Journal of Physical Oceanography, 43(2):366-381.
Shchepetkin A F, Mcwilliams J C. 2003. A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate.Journal of Geophysical Research Oceans, 108(C3):3 090.
Shchepetkin A F, Mcwilliams J C. 2005. The regional oceanic modeling system (ROMS):a split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean Modelling, 9(4):347-404.
Shen J, Medjo T T, Wang S. 1999. On a wind-driven, doublegyre, quasi-geostrophic ocean model:numerical simulations and structural analysis. Journal of Computational Physics, 155(2):387-409.
Simonnet E, Ghil M, Ide K, Temam R, Wang S H. 2003. Lowfrequency variability in shallow-water models of the wind-driven ocean circulation. Part Ⅱ:time-dependent solutions. Journal of Physical Oceanography, 33(4):729-752.
Speich S, Dijkstra H, Ghil M. 1995. Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation. Nonlinear Processes in Geophysics, 2(3-4):241-268.
Sura P, Penland C. 2002. Sensitivity of a double-gyre ocean model to details of stochastic forcing. Ocean Modelling, 4(3):327-345.
Van Scheltinga A D T, Dijkstra H A. 2008. Conditional nonlinear optimal perturbations of the double-gyre ocean circulation. Nonlinear Processes in Geophysics, 15(5):727-734.
Wang Q, Ma L B, Xu Q Q. 2013a. Optimal precursor of the transition from Kuroshio large meander to straight path.Chinese Journal of Oceanology and Limnology, 31(5):1 153-1 161.
Wang Q, Mu M, Dijkstra H A. 2012. Application of the Conditional Nonlinear Optimal Perturbation Method to the Predictability Study of the Kuroshio Large Meander.Advances in Atmospheric Sciences, 29(1):118-134.
Wang Q, Mu M, Dijkstra H A. 2013b. The similarity between optimal precursor and optimally growing initial error in prediction of Kuroshio large meander and its application to targeted observation. Journal of Geophysical Research:Oceans, 118(2):869-884.
Wang Q, Tang Y M, Pierini S, Mu M. 2017. Effects of singularvector-type initial errors on the short-range prediction of kuroshio extension transition processes. Journal of Climate, 30(15):5 961-5 983.
Warner J C, Geyer W R, Lerczak J A. 2005b. Numerical modeling of an estuary:A comprehensive skill assessment.Journal of Geophysical Research Oceans, 110(C5):C05001.
Warner J C, Sherwood C R, Arango H G, et al. 2005a.Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modelling, 8(1):81-113.
Wen S C, Yuan S J, Mu B, Li H Y, Ren J H. 2015. PCGD:Principal components-based great deluge method for solving CNOP. In:2015 IEEE Congress on Evolutionary Computation (CEC). IEEE, Sendai, Japan.
Wilkin J L, Arango H G, Haidvogel D B, et al. 2005. A regional ocean modeling system for the Long-term Ecosystem Observatory. Journal of Geophysical Research Oceans, 110(C6):C06S91.
Yu J S. 1998. Setting up and calibration analysis of three dimensional ocean current forecasting mode (2/4). Accessed on 2012-12-30. (in Chinese)
Zhang K, Wang Q, Mu M, Liang P. 2016. Effects of optimal initial errors on predicting the seasonal reduction of the upstream Kuroshio transport. Deep Sea Research Part I:Oceanographic Research Papers, 116:220-235.
Zhang L L, Yuan S J, Mu B, Zhou F F. 2017b. CNOP-based sensitive areas identification for tropical cyclone adaptive observations with PCAGA method. Asia-Pacific Journal of Atmospheric Sciences, 53(1):63-73.
Zhang X, Mu M U, Pierini S. 2017a. Optimal precursors triggering the kuroshio extension state transition obtained by the conditional nonlinear optimal perturbation approach. Advances in Atmospheric Sciences, 34(6):685-699.