Proper orthogonal and dynamic mode decomposition of sunspot data

High-resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here, we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape.