A two-time-level split-explicit ocean circulation model (MASNUM) and its validation
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A two-time-level split-explicit ocean circulation model (MASNUM) and its validation HAN Lei1,2* 1 2
First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China Institute of Oceanography, Chinese Academy of Sciences, Qingdao 266071, China
Received 13 August 2013; accepted 26 November 2013 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014
Abstract A two-time-level, three-dimensional numerical ocean circulation model (named MASNUM) was established with a two-level, single-step Eulerian forward-backward time-differencing scheme. A mathematical model of large-scale oceanic motions was based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method was adopted to replace the most preferred leapfrog scheme as the time-differencing method for both barotropic and baroclinic modes. The forward-backward method is of second-order of accuracy, computationally efficient by requiring only one function evaluation per time step, and free of the computational mode inherent in the three-level schemes. This method is superior to the leapfrog scheme in that the maximum time step of stability is twice as large as that of the leapfrog scheme in staggered meshes thus the computational efficiency could be doubled. A spatial smoothing method was introduced to control the nonlinear instability in the numerical integration. An ideal numerical experiment simulating the propagation of the equatorial Rossby soliton was performed to test the amplitude and phase error of this new model. The performance of this circulation model was further verified with a regional (northwest Pacific) and a quasi-global (global ocean simulation with the Arctic Ocean excluded) simulation experiments. These two numerical experiments show fairly good agreement with the observations. The maximum time step of stability in these two experiments were also investigated and compared between this model and that model which adopts the leapfrog scheme. Key words: ocean circulation model, forward-backward method, equatorial Rossby soliton, Yellow Sea Cold Water Mass Citation: Han Lei. 2014. A two-time-level split-explicit ocean circulation model (MASNUM) and its validation. Acta Oceanologica Sinica, 33(11): 11–35, doi: 10.1007/s13131-014-0553-z
1 Introduction In the selection of the time stepping method, most of the three-dimensional circulation models adopt three-level time differencing scheme in their algorithm system, among which the leapfrog scheme is most preferred (Haidvogel and Beckmann, 1997; Kantha and Clayson, 2000). None of the threedimensional circulation models employ an explicit two-level temporal discretization scheme (The Crank-Nicolson scheme adopted in GBM model is a two-level but implicit scheme). Three-time-level schemes refer to the method using data from two previous time levels to step forward to the next time level. They are preferred in the geophysical circulation models because it is str
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