  We seek to estimate the average level of MHD turbulence near coronal mass
ejection (CME) fronts as they propagate from the Sun to the Earth. We examine
the cosmic ray data from the GRAPES-3 tracking muon telescope at Ooty, together
with the data from other sources for three well observed Forbush decrease
events. Each of these events are associated with frontside halo Coronal Mass
Ejections (CMEs) and near-Earth magnetic clouds. In each case, we estimate the
magnitude of the Forbush decrease using a simple model for the diffusion of
high energy protons through the largely closed field lines enclosing the CME as
it expands and propagates from the Sun to the Earth. We use estimates of the
cross-field diffusion coefficient $D_{\perp}$ derived from published results of
extensive Monte Carlo simulations of cosmic rays propagating through turbulent
magnetic fields. Our method helps constrain the ratio of energy density in the
turbulent magnetic fields to that in the mean magnetic fields near the CME
fronts. This ratio is found to be $\sim$ 2% for the 11 April 2001 Forbush
decrease event, $\sim$ 6% for the 20 November 2003 Forbush decrease event and
$\sim$ 249% for the much more energetic event of 29 October 2003.
