Long-lived rotational and meridional flows are important ingredients of the solar cycle .
Magnetic field images have typically been used to measure these flows on the solar surface by cross-correlating thin longitudinal strips or square patches across sufficiently long time gaps .
Here , I use one month of SDO/HMI line-of-sight magnetic field observations , combined with the SWAMIS magnetic feature tracking algorithm to measure the motion of individual features in these magnetograms .
By controlling for perturbations due to short-lived flows and due to false motions from feature interactions , I effectively isolate the long-lived flows traced by the magnetic features .
This allows me to produce high-fidelity differential rotation measurements with well-characterized variances and covariances of the fit parameters .
I find a sidereal rotational profile of ( 14.296 \pm 0.006 ) + ( -1.847 \pm 0.056 ) \sin ^ { 2 } b + ( -2.615 \pm 0.093 ) \sin ^ { 4 } b , with units of \textrm { deg d } ^ { -1 } , and a large covariance \sigma _ { BC } ^ { 2 } = -4.87 \times 10 ^ { -3 } ( \textrm { deg d } ^ { -1 } ) ^ { 2 } .
I also produce medium-fidelity measurements of the much weaker meridional flow that is broadly consistent with previous results .
This measurement shows a peak flow of 16.7 \pm 0.6 \text { m s } ^ { -1 } at latitude b = 45 \degree but is insufficiently characterized at higher latitudes to ascertain whether the chosen functional form 2 \cos b \sin b is appropriate .
This work shows that measuring the motions of individual features in photospheric magnetograms can produce high precision results in relatively short time spans , and suggests that high resolution non-longitudinally averaged photospheric velocity residual measurements could be produced to compare with coronal results , and to provide other diagnostics of the solar dynamo .