Evolution of the magnetic field strength at the dynamo surface averaged in time, using the scaling laws and calculating the average value of the magnetic field over different relative thicknesses q, around r_m (green, blue, orange, and red). The error bars are associated with the radial variation and are larger for thinner integration shells over which we evaluated Eq. (18). The dotted lines show the corresponding best-fit power laws. The solid lines indicate Eq. (15) applied to our MESA output (pink), and the prediction by Reiners & Christensen (2010) (gray).