The Degree of Machenhauer Balance in a Climate Model

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

Time series of normal mode coefficients were determined by projection of data produced at every time step for 64 days of a long climate simulation with the NCAR Community Climate Model. From these, the coefficient tendencies, linear forcing, and nonlinear forcing were calculated. Given this nonlinear forcing, the error due to neglect of the time tendency term by Machenhauer's balance scheme was then determined along with errors for higher order schemes in which higher order tendencies were neglected.

Results indicate that the errors are typically less than 10% of the true mode amplitudes for most external and first-internal modes. As shallower modes are considered, typical errors are 1arger: for the fourth vertical mode a typical error is 30%, although greater for the Kelvin modes. Higher-order schemes (through sixth order) only improve the description of balance for some modes with resonant periods shorter than 10 hours. For other modes, the errors increase with the order of the scheme.

Abstract

Time series of normal mode coefficients were determined by projection of data produced at every time step for 64 days of a long climate simulation with the NCAR Community Climate Model. From these, the coefficient tendencies, linear forcing, and nonlinear forcing were calculated. Given this nonlinear forcing, the error due to neglect of the time tendency term by Machenhauer's balance scheme was then determined along with errors for higher order schemes in which higher order tendencies were neglected.

Results indicate that the errors are typically less than 10% of the true mode amplitudes for most external and first-internal modes. As shallower modes are considered, typical errors are 1arger: for the fourth vertical mode a typical error is 30%, although greater for the Kelvin modes. Higher-order schemes (through sixth order) only improve the description of balance for some modes with resonant periods shorter than 10 hours. For other modes, the errors increase with the order of the scheme.

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