In this paper, simulations of the quasi-geostrophic zonal channel are analysed using the data-driven methods of Sparse Identification of Nonlinear Dynamics (SINDy) and Linear Regression. The shear-driven zonal channel is simulated by a stratified quasi-geostrophic model in an eddy-resolving turbulent regime with re-entry boundary conditions. The simulation results are compressed using the classic Proper Orthogonal Decomposition (POD) in the statistically stationary period, and the time dependent coefficients of the reduced-order model are selected based on their contributions in total kinetic and potential energy of the system. The selected temporal coefficients are next provided for the SINDy and Linear Regression codes to identify linear dynamics. Finally, the flow field is reconstructed using POD expansion with time coefficients predicted by SINDy and Linear Regression models and the results are compared with original simulations beyond the training window in terms of time-averaged cross-correlations.