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Abstract Meridional circulation regulates the Sun’s interior dynamics and magnetism. While it is well accepted that meridional flows are poleward at the Sun’s surface, helioseismic observations have yet to provide a definitive answer for the depth at which those flows return to the equator, or the number of circulation cells in depth. Here, we explore the observability of multiple circulation cells stacked in radius. Specifically, we examine the seismic signature of several meridional flow profiles by convolving time–distance averaging kernels with mean flows obtained from a suite of 3D hydrodynamic simulations. At mid and high latitudes, we find that weak flow structures in the deep convection zone can be obscured by signals from the much stronger surface flows. This contamination of 1–2 m s⁻¹is caused by extended side lobes in the averaging kernels, which produce a spurious equatorward signal with flow speeds that are 1 order of magnitude stronger than the original flow speeds in the simulations. At low latitudes, the flows in the deep layers of the simulations are stronger (>2 m s⁻¹) and multiple cells across the convection zone can produce a sufficiently strong signal to survive the convolution process. Now that meridional flows can be measured over two decades of data, the uncertainties arising from convective noise have fallen to a level where they are comparable in magnitude to the systematic biases caused by nonlocal features in the averaging kernels. Hence, these systematic errors are beginning to influence current helioseismic deductions and need broader consideration. 

Abstract Cyclical variations of the solar magnetic fields, and hence the level of solar activity, are among the top interests of space weather research. Surface flows in global-scale, in particular differential rotation and meridional flows, play important roles in the solar dynamo that describes the origin and variation of solar magnetic fields. In principle, differential rotation is the fundamental cause of dipole field formation and emergence, and meridional flows are the surface component of a longitudinal circulation that brings decayed field from low latitudes to polar regions. Such flows are key inputs and constraints of observational and modeling studies of solar cycles. Here, we present two methods, local correlation tracking (LCT) and machine learning-based self-supervised optical flow methods, to measure differential rotation and meridional flows from full-disk magnetograms that probe the photosphere and $$\text{H}\alpha$$ H α images that probe the chromosphere, respectively. LCT is robust in deriving photospheric flows using magnetograms. However, we found that it failed to trace flows using time-sequence $$\text{H}\alpha $$ H α data because of the strong dynamics of traceable features. The optical flow methods handle $$\text{H}\alpha $$ H α data better to measure the chromospheric flow fields. We found that the differential rotation from photospheric and chromospheric measurements shows a strong correlation with a maximum of $$2.85~\upmu \text{rad}\,\text{s}^{-1}$$ 2.85 μrad s − 1 at the equator and the accuracy holds until $$60^{\circ }$$ 60 ∘ for the MDI and $$\text{H}\alpha$$ H α , $$75^{\circ }$$ 75 ∘ for the HMI dataset. On the other hand, the meridional flow deduced from the chromospheric measurement shows a similar trend as the concurrent photospheric measurement within $$60^{\circ }$$ 60 ∘ with a maximum of $$20~\text{m}\,\text{s}^{-1}$$ 20 m s − 1 at $$40^{\circ }$$ 40 ∘ in latitude. Furthermore, the measurement uncertainties are discussed. 

Abstract We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.