An error evaluation on the vertical velocity algorithm in POM
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An error evaluation on the vertical velocity algorithm in POM 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 14 January 2013; accepted 26 November 2013 ©The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2014
Abstract A time splitting technique is common to many free surface ocean models. The different truncation errors in the equations of the internal and external modes require a numerical adjustment to make sure that algorithms correctly satisfy continuity equations and conserve tracers quantities. The princeton ocean model (POM) has applied a simple method of adjusting the vertical mean of internal velocities to external velocities at each internal time step. However, due to the Asselin time filter method adopted to prevent the numerical instability, the method of velocity adjustment used in POM can no longer guarantee the satisfaction of the continuity equation in the internal mode, though a special treatment is used to relate the surface elevation of the internal mode with that of the external mode. The error is proved to be a second-order term of the coefficient in the Asselin filter. One influence of this error in the numerical model is the failure of the kinetic boundary condition at the sea floor. By a regional experiment and a quasi-global experiment, the magnitudes of this error are evaluated, and several sensitivity tests of this error are performed. The characteristic of this error is analyzed and two alternative algorithms are suggested to reduce the error. Key words: mode splitting, asselin filter, velocity adjustment method, POM Citation: Han Lei. 2014. An error evaluation on the vertical velocity algorithm in POM. Acta Oceanologica Sinica, 33(7): 12–20, doi: 10.1007/s13131-014-0505-7
1 Introduction The time splitting technique is common to many free surface ocean models. Rather than solving three-dimensional equations with a short time step required by the CourantFriedrichs-Lewy (CFL) stability condition (Courant et al., 1967), it is more efficient to compute barotropic modes separately in a simplified two-dimensional model. The time step in a complete three-dimensional model could be relaxed to tens of times longer than before removing fast modes. The two-dimensional model dealing with the barotropic modes is known as the “external mode” (also known as the barotropic mode); while the three-dimensional model free of fast modes is called the “internal mode” (also known as the baroclinic mode). The external mode usually steps forward with a short time interval ǻtE, while the internal mode which undertakes most of the computations steps forward with a much longer time interval ǻtI (Higdon and Bennett, 1996; Higdon and de Szoeke, 1997). The ratio of ǻtI to ǻtE could be set 5–10 in estuary, and 40 in open ocean (Kantha and Clayson, 2000). According to Ezer et al. (2002), the ratio could be in the range of 20–80. The system of governing equa
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