  We study effect of noise on the tunneling process of the magnetization in a
sweeping field from the viewpoint of the nonadiabatic transition. The tunneling
probability depends on the properties of the noise, e.g. the direction, the
amplitude, and the relaxation time of the autocorrelation function. We
investigate the tunneling process in the presence of noise by solving the
time-dependent Schr$\rm{\ddot{o}}$dinger equation numerically, and analyze its
parameter dependence. We estimate the effective tunneling gap making use of the
Landau-Zener-St$\rm{\ddot{u}}$ckelberg (LZS) formula. The dependence of the gap
on the sweeping velocity reproduces the corresponding experimental data
qualitatively. For fast sweeping field the estimated gap has no velocity
dependence and this gap seems to give the true gap. We, however, show that a
correction for the estimated energy gap is necessary and we propose an
correction formula.
