The existence of a turbulent small-scale solar surface dynamo is likely, considering existing numerical and laboratory experiments, as well as comparisons of a small-scale dynamo in MURaM simulations with Hinode obser-vations. We find the observed peaked probability distribution function (PDF) from Stokes-V magnetograms is consistent with a monotonic PDF of the ac-tual vertical field strength. The cancellation function of the vertical flux density from a Hinode SP observation is found to follow a self-similar power law over two decades in length scales down to the ≈200 km resolution limit. This provides observational evidence that the scales of magnetic structuring in the photosphere extend at least down to 20 km. From the power law, we determine a lower bound for the true quiet-Sun mean vertical unsigned flux density of ≈43 G, consistent with our numerically-based estimates that 80% or more of the vertical unsigned flux should be invisible to Stokes— V observations at a resolution of 200 km ow-ing to cancellation. Our estimates significantly reduce the order-of-magnitude discrepancy between Zeeman- and Hanle-based estimates.
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