Modeled inflows and travel-time perturbations at mid-latitudes as a function of time. Panels a–c: averages of , , and from Figs. 7a–c over the latitudes λ = 20° −35° in each hemisphere (thin lines). The errors on the models, estimated from the misfits, are about 0.6 m s⁻¹ for panel a, 0.04 s for panel b, and 0.03 s for panel c; they are not shown here. For comparison, the corresponding , −τ^AR, and from Figs. 5d–f are overplotted in thick lines; the data in the first and last six months are not shown because the edge effects become visible due to the one-year temporal smoothing of the background flows. Panel d: 13-month running mean of the hemispheric monthly sunspot numbers. The red (respectively blue) filling indicates an excess of sunspot numbers in the northern (respectively southern) hemisphere.