We calculate the steady-state linear response matrix of a two-layer quasi-geostrophic model (two-layer QG model). We impose the multisine excitation, which can effectively detect the magnitude of nonlinear distortions and attain a high signal-to-noise ratio (SNR). This method has recently been introduced to atmospheric science, but has not been applied to the linearization of the two-layer QG model yet. By considering periodic excitations, this method produces a linearization applicable to a wider range of problems. We will examine the frequency dependence of the linear response matrix to evaluate the memory of the two-layer QG model. We will combine the linear response at different frequencies to give a steady-state linear response matrix. The steady-state linear response matrix can be applied to construct time-invariant forcings to force a specified mean state of the model without directly acting on the eddies, and therefore, help to measure the response of eddies to mean state changes and help to gain a better understanding of wave–mean flow interactions.

multisine excitation, two-layer quasi-geostrophic model, system identification