Optimization of objective function (left) and increase in accuracy (right) as the iterative minimization proceeds, at a fixed sampling frequency of ∼1 month (33 days), for varying assimilation window widths. ﹩{N}_{t}^{o}=61,121,181,{\rm{}}\;{\rm{and}}\;{\rm{}}241﹩ correspond to sampling windows of width 0.5, 1.0, 1.5, and 2.0 solar cycle(s), respectively. Here and on the plots that follow, we indicate case 1, case 2, and case 3 with solid lines, crosses, and broken lines, respectively. The number of observation points in latitude is the same for all cases (﹩{N}_{\theta }^{o}=63﹩). The convergence rate increases with the number of iterations (i.e., when the predicted state gets closer to the true state).