Long-Term Trends in Subsurface Flows of Solar Cycle 23 to 25

We study the long-term variation of the zonal and meridional flows from Solar Cycle 23 to 25 derived with ring-diagram analysis applied to Global Oscillation Network Group (GONG) and Helioseismic and Magnetic Imager (HMI) Dopplergrams. We focus mainly on the subsurface flows averaged over depths from 2.0 Mm to 11.6 Mm since their long-term variations are sufficiently similar. First, we examine their temporal variations for systematic artifacts. We find that the GONG-derived zonal flows increase almost linearly with time until about 2020, which we correct with a linear regression. Then we determine the average differences between the GONG- and HMI-derived flows. The average offset is 0.15 +/- 0.53\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0.15 \pm 0.53$\end{document} m s-1 for the zonal flow and 0.65 +/- 0.08\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0.65 \pm 0.08$\end{document} m s-1 for the meridional flow within +/- 30.0 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\pm 30.0<^>{\circ }$\end{document} latitude. The average difference of the meridional flow is nearly constant with latitude in this range, whereas that of the zonal flow varies similarly to that of the magnetic activity. At latitudes of 45.0 degrees and higher, the differences increase and are larger than those at lower latitudes, which is most likely due to the combined effect of different spatial resolution between GONG and HMI and geometric projection effects. Finally, we combine the GONG- and HMI-derived flows and find, as expected, that the solar-cycle variation is the dominant long-term variation. At each latitude within +/- 30.0 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\pm 30.0<^>{\circ }$\end{document}, the meridional-flow pattern appears ahead of the zonal-flow pattern by an average lag of 0.926 +/- 0.126\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0.926 \pm 0.126$\end{document} years. The equatorward and poleward branches of the solar-cycle variation occur at 52.5 degrees with the poleward branches present near 60.0 degrees and the equatorward ones at lower latitudes. The zonal flows at 52.5 degrees and 60.0 degrees show an additional trend and decrease by 2.9 +/- 0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2.9 \pm 0. 3$\end{document} m s-1 over 11 years. This decrease might nevertheless be related to the solar cycle and imply that the flow amplitudes are anticorrelated with the strength of the associated solar cycle.