  Utilizing a splitting of geometric flows on surfaces introduced by Buzano and
Rupflin, we present a general scheme to prove blow up criteria for such
geometric flows. A vital ingredient is a new compactness theorem for families
of metrics on surfaces with a uniform bound on their volumes, square integrals
of their curvatures and injectivity radii. In particular we prove blow up
criteria for the harmonic Ricci flow and for the spinor flow on surfaces.
