This study utilizes the multisine excitation method to calculate the steady-state linear response matrix of a two-layer quasi-geostrophic model (two-layer QG model) and establish the relationship between changes in the system's mean state and external forcing. The multisine excitation method effectively controls nonlinear distortion and improves the signal-to-noise ratio. The multisine excitation method combined with state-space model is a system identification technique recently introduced into the atmospheric sciences. However, it has not yet been applied to the linearization of the two-layer QG model. The steady-state linear response matrix obtained in this study exhibits high accuracy, with an accuracy rate exceeding 96% for the training data and exceeding 77% for the response to time invariant forcing on EOF1. In contrast, for time invariant forcing on EOF1, the accuracy rate for the Principal Oscillation Pattern method is less than 72%, while that for the Dynamic Mode Decomposition method is -3%. It is believed that the steady-state linear response matrix obtained by this method offers the advantage of high accuracy. The matrix will assist in constructing specific forcing conditions for the study of wave-mean flow interactions, inducing specific changes in the system's mean state; such forcing does not directly alter the system's wave dynamics. In numerical experiments, it helps accurately calculate the effect of changes in the mean state on the wave dynamics. The linearization strategy developed in this study holds potential for application to more complex non-linear systems.

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