Improved Measurements of the Sun's Meridional Flow and Torsional Oscillation from Correlation tracking on MDI \& HMI magnetograms

The Sun's axisymmetric flows, differential rotation and meridional flow, govern the dynamics of the solar magnetic cycle and variety of methods are used to measure these flows, each with its own strengths and weaknesses. Flow measurements based on cross-correlating images of the surface magnetic field have been made since the 1970s which require advanced numerical techniques that are capable of detecting movements of less than the pixel size in images of the Sun. We have identified several systematic errors in addition to the center-to-limb effect that influence previous measurements of these flows and propose numerical techniques that can minimize these errors by utilizing measurements of displacements at several time-lags. Our analysis of line-of-sight magnetograms from the {\em Michelson Doppler Imager} (MDI) on the ESA/NASA {\em Solar and Heliospheric Observatory} (SOHO) and {\em Helioseismic and Magnetic Imager} (HMI) on the NASA {\em Solar Dynamics Observatory} (SDO) shows long-term variations in the meridional flow and differential rotation over two sunspot cycles from 1996 to 2020. These improved measurements can serve as vital inputs for solar dynamo and surface flux transport simulations.