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Long-lived rotational and meridional flows are important ingredients of thesolar cycle. Magnetic field images have typically been used to measure theseflows on the solar surface by cross-correlating thin longitudinal strips orsquare patches across sufficiently long time gaps. Here, I use one month ofSDO/HMI line-of-sight magnetic field observations, combined with the SWAMISmagnetic feature tracking algorithm to measure the motion of individualfeatures in these magnetograms. By controlling for perturbations due toshort-lived flows and due to false motions from feature interactions, Ieffectively isolate the long-lived flows traced by the magnetic features. Thisallows me to produce high-fidelity differential rotation measurements withwell-characterized variances and covariances of the fit parameters.I find asidereal rotational profile of$(14.296\pm0.006)+(-1.847\pm0.056)\sin^{2}b+(-2.615\pm0.093)\sin^{4}b$, withunits of $\textrm{ deg d}^{-1}$, and a large covariance$\sigma_{BC}^{2}=-4.87\times10^{-3}(\textrm{ deg d}^{-1})^{2}$. I also producemedium-fidelity measurements of the much weaker meridional flow that is broadlyconsistent with previous results. This measurement shows a peak flow of$16.7\pm0.6\text{ m s}^{-1}$ at latitude $b=45^\circ$ but is insufficientlycharacterized at higher latitudes to ascertain whether the chosen functionalform $2\cos b\sin b$ is appropriate. This work shows that measuring the motionsof individual features in photospheric magnetograms can produce high precisionresults in relatively short time spans, and suggests that high resolutionnon-longitudinally averaged photospheric velocity residual measurements couldbe produced to compare with coronal results, and to provide other diagnosticsof the solar dynamo.

Measurements of Solar Differential Rotation and Meridional Circulation from Tracking of Photospheric Magnetic Features