Total solar magnetic flux: Dependence on spatial resolution of magnetograms

The variability of the solar radiative output is tied to the evolution of the surface magnetic field. Irradiance changes on time-scales of the solar rotation are governed by the varying distribution of the magnetic features and the evolution of sunspots and individual active regions, whereas the total amount of magnetic flux in particular small-scale magnetic elements seems to dominate the irradiance variations on the time scale of the solar cycle. Possibly of even greater relevance for climate on Earth are secular variations of solar irradiance, which are at least partly caused by changes in the quiet-Sun magnetic flux on long time scales. Using NSO/Kitt Peak synoptic charts Harvey (1994) found that the total magnetic flux in active regions at activity maximum is about 3 times higher than the flux at activity minimum. The size of small-scale magnetic elements is, however, far below the resolution of currently obtainable magnetograms. At the same time, their distribution on the solar surface is highly non-uniform, with magnetic elements of opposite polarities often being grouped close together. This leads to an apparent cancellation of the flux within a relatively large pixel of a Kitt Peak synoptic chart and underestimates the total magnetic flux, mainly in the quiet Sun. Using MDI full-disc and high-resolution magnetograms and artificially reducing their spatial resolution by binning several pixels together we study the influence of the resolution on the measured total magnetic flux.