Abstract
A method for finding the most unstable eigenmodes in linear models using the breeding technique was developed. The breeding technique was extended to allow for the calculation of complex eigenvalues and eigenvectors of the linear model operator without involving computationally expensive matrix manipulations. While the breeding method finds the most unstable modes, multiple planetary basin modes may be found by removing the leading modes using the adjoint model. To test the sensitivity of basin modes to model formulation, the method was applied for the calculation of the gravest planetary basin modes in a reduced-gravity linear shallow water model with complex basin geometry and background circulation. It was found that the leading basin modes are not sensitive to the form of the dissipation or model resolution, suggesting that the decadal modes are robust. However, the properties of the low-frequency modes are strongly affected by the basin geometry and the mean flow.
