Extended Data Figure 5: Solutions for the odd harmonics using random zonal wind profiles and a fixed vertical profile.

a–f, Solutions (blue) for J₃, J₅, J₇ and J₉ for flows with 1,000 different artificial meridional profiles of the zonal wind (as in Extended Data Fig. 3), and the vertical profile held fixed with H = 2,000 km, ΔH = 1,500 km and α = 1. The Juno measurements are shown in red with their corresponding uncertainty ellipse. The solution with these parameters and using Jupiter’s observed cloud-level zonal wind profile is shown in black with the corresponding uncertainty ellipse. g, The cost function for all different meridional profiles explored, with the red line corresponding to the solution with the Jupiter zonal wind profile. This shows that when no optimization is done (which takes into consideration the relative measurement error of the different harmonics), the solutions are spread equally over all four quadrants in these phase spaces (unlike in Extended Data Fig. 4). Only one solution has a lower cost function (green).