  We present direct numerical simulations and Lagrangian averaged (also known
as alpha-model) simulations of forced and free decaying magnetohydrodynamic
turbulence in two dimensions. The statistics of sign cancellations of the
current at small scales is studied using both the cancellation exponent and the
fractal dimension of the structures. The alpha-model is found to have the same
scaling behavior between positive and negative contributions as the direct
numerical simulations. The alpha-model is also able to reproduce the time
evolution of these quantities in free decaying turbulence. At large Reynolds
numbers, an independence of the cancellation exponent with the Reynolds numbers
is observed.
